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A kinetic growth model for Saccharomyces cerevisiae grown under redox potential-controlled very-high-gravity environment
Biochemical Engineering Journal 56 (2011) 63–68
Contents lists available at ScienceDirect
Biochemical Engineering Journal journal homepage: www.elsevier.com/locate/bej
A kinetic growth model for Saccharomyces cerevisiae grown under redox potential-controlled very-high-gravity environment Chen-Guang Liu a , Yen-Han Lin b,∗ , Feng-Wu Bai a a b
School of Bioscience and Bioengineering, Dalian University of Technology, Dalian, Liaoning 116023, China Department of Chemical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, SK S7N5A9, Canada
a r t i c l e
i n f o
Article history: Received 24 December 2010 Received in revised form 29 March 2011 Accepted 14 May 2011 Available online 23 May 2011 Keywords: Saccharomyces cerevisiae Ethanol Kinetic models Very-high-gravity fermentation Redox potential Operating diagram
a b s t r a c t A growth kinetic model for redox potential-controlled very-high-gravity (VHG) fermentation was developed. The model is semi-empirical and two important VHG fermentation operating conditions including glucose feed and redox potential level were incorporated in the model. The model consists of a substrate inhibition term and a product toxification term. A two-step parameter-estimating strategy was proposed and implemented. In the first step, the first few experimentally collected data points were used to estimate parameters relating to the substrate inhibition term; in the second step, the complete data set was used to estimate parameters relating to the product toxification term. The developed growth model could fit the original data with an R2 value >0.95. Three operating diagrams were constructed by using the results generated from the developed model. Each respective diagram could be used to select the best operating condition for the shortest fermentation time, the highest final ethanol concentration, or the highest fermentation efficiency. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Fuel alcohol is the most widely used petroleum-based fuel alternative nowadays. It is mainly applied to the transportation sector to reduce carbon dioxide emission, and is regarded as an environmentally friendly and sustainable fuel substitute due to its net-zero carbon discharge. Fuel alcohol is produced by Saccharomyces cerevisiae in fermentation with the consumption of grain-based crops or sugar canes. Ethanol is the primary metabolite secreted by yeast; the more sugar present during fermentation, the more ethanol produced. Very-high-gravity (VHG) fermentation is a technology where the fermenter is over-supplemented by glucose for ethanol production. The typical species used for this purpose is ethanol-tolerating S. cerevisiae. Hence, high ethanol productivity and significant energy savings can be realized [1,2]. During the course of VHG ethanol fermentation, yeast simultaneously encounters physical, chemical, and biological stresses [3]. Particularly, in the late stage of stationary phase, abrupt cell death attributed to the accumulated ethanol in the fermenter is commonly observed, and consequently prolongs the fermentation time. One approach to combat the ethanol toxicity during batch fermentation is to provide oxygen
∗ Corresponding author. Tel.: +1 306 966 4764; fax: +1 306 966 4777. E-mail address: [email protected] (Y.-H. Lin). 1369-703X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.bej.2011.05.008
for yeast to enhance yeast activity [4]. On the other hand, an over-aerated fermenter may alter intracellular metabolic pathways, leading to low ethanol production [5]. Measuring dissolved oxygen at low levels in a large fermenter is a challenge [6]. One of the reliable and practical alternatives is the redox potential measurement [7,8]. The redox potential is an indicator of the net balance of overall reduction and oxidation in a solution. A high redox potential level signifies a high tendency of losing electrons or the presence of a high level of dissolved oxygen, and/or vice versa. The application of redox potential to cultivate organisms at different micro-aerobic environments has been reported [9–12]. To model yeast growth kinetics under VHG fermentation, one requires an understanding of substrate osmosis resulting from high glucose feed which later results in the buildup of ethanol that inhibits and adversely toxifies yeast, thus causing the growth arrest. Due to the hidden biological complexity under VHG conditions, the common growth models were not applicable [13,14]; specifically, when the redox potential was implemented to modulate reduction–oxidation balance within yeast. In this study, we developed a new semi-empirical growth kinetic model that purposefully took glucose feeds and redox potential levels into consideration. Based on experimental observations [15], a two-step parameterestimating strategy was proposed and implemented to estimate kinetic parameters pertinent to yeast growth, ethanol production, and glucose consumption. Accordingly, operating diagrams were
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C.-G. Liu et al. / Biochemical Engineering Journal 56 (2011) 63–68
Nomenclature a0 , a1 , a2 k1 k2 Ki Ks m ˆ m ¯ m mpred ORP P Po Pmax r
S So t X YSP
regression coefficients defined in Eq. (3) growth-associated parameter (g/l/h) nongrowth-associated parameter (g/l/h) glucose inhibition constant (g/l) half saturation constant (g/l) metabolite concentration (g/l) maximum metabolite concentration (g/l) average metabolite concentration (g/l) predicted metabolite concentration (g/l) redox potential level (mV) ethanol concentration at time t (g/l) ethanol concentration at time 0 (g/l) maximum tolerable ethanol concentration (g/l) positive, maximum specific metabolite production rate (1/h); negative, maximum specific metabolite consumption rate (1/h) glucose concentration at time t (g/l) glucose feed or initial glucose concentration (g/l) time (h) biomass concentration (g/l) yield of glucose to ethanol (g/g)
Greek letters ˛ degree of ethanol toxicity order of growth association ˇ1 ˇ2 order of nongrowth association P ethanol production (g/l) −S glucose consumption (g/l) specific growth rate (1/h) max maximum specific growth rate (1/h)
constructed to assist the fuel alcohol industry to locate the most suitable operating conditions for VHG ethanol fermentation process.
2. Materials and methods 2.1. Strain, growth media, fermentation, and sample analysis Strain, growth media, and sample analysis were previously reported [15]. Briefly, an industrial S. cerevisiae strain (Ethanol RedTM ) was pre-cultured overnight and cultivated in a jar fermenter. In addition to 300 ± 8.06, 253 ± 3.77, or 203 ± 4.75 g glucose/l, the growth medium consisted of trace mineral salts, vitamin cocktail, urea, yeast extract, and sodium glutamate. The fermentation broth was collected every 6 h, and the violet red staining technique was implemented to differentiate viable and dead cells. As a result, cell viability was estimated. By using HPLC, the supernatant portion of the broth was used to quantify the residual glucose, ethanol, and other metabolites.
collected from batch redox potential-controlled VHG fermentation. The curve is expressed as
m dm =r 1− dt ˆ m
m
(1)
When the r value is positive, it is called the maximum specific metabolite production rate; when negative, it is called the maximum specific metabolite consumption rate. We used our previously reported data [15] as raw data and smoothed it by the above-noted logistic growth curve. VHG fermentation characterizes high glucose feed where substrate-induced osmotic stress is observed, leading to a long lag phase. To simulate this phenomenon, a substrate inhibition model (the first term on the right hand side of Eq. (2)) was adopted. As fermentation continues, the buildup of ethanol inhibits and later toxifies yeast propagation, resulting in drastic reduction in yeast viability. To simulate such an adverse effect on a yeast population, a product toxification model (the second term on the right hand side of Eq. (2)) was incorporated and shown below: = max =0
S P 1− Pmax S + KS + S 2 /Ki
˛ when P < Pmax
(2)
when P > Pmax
Refer to Fig. 2 as reported in [15], the glucose utilization rate correlates to the glucose feed; that is, the lower the glucose feed (So ), the faster the fermentation rate is attainable. Further refer to Fig. 3 in [15], it illustrates that the yeast viability can be modulated by varying redox potential levels (ORP). It is known that ethanol synthesis by yeast is classified as primary fermentation, meaning that the higher the viable population, the more ethanol would be expected. As a result, a higher final ethanol concentration could be obtained. The final ethanol concentration refers to ethanol obtained at the completion of fermentation. Hence, a linear relationship among the glucose feed, the redox potential level, and the maximum ethanol concentration was proposed and expressed as follows: Pmax = a0 + a1 S0 + a2 ORP
(3)
Refer to Fig. 1a, the amount of ethanol produced is directly associated with the population size of yeast. When the biomass concentration is greater than 7.4 g/l (see dotted line shown in Fig. 1a, the yeast growth slows down and nearly stops, and the ethanol continues to accumulate. Based on these observations, we proposed Eq. (4) to describe yeast growth kinetics:
dX dP = k1 dt dt
ˇ1
+ k2 X ˇ2
(4)
The first two terms on the right-hand side of Eq. (4) represent growth-associated and non-growth-associated ethanol production, respectively. While plotting the change of ethanol (P) versus the change of glucose (−S), a linear relationship is observed (Fig. 1b). Accordingly, a yield coefficient (YSP ) was defined and presented in Eq. (5):
2.2. Data processing and modeling −S = YSP P Experimentally collected data are typically discrete. However when applied to numerical predictions directly, a significant discrepancy between actual and predicted data points occurs. Hence, the data smoothing approach is necessary before conducting numerical calculations. There are many sigmoidal equations available to conduct data smoothing. In this study, we chose a three-parameter logistic growth curve to model metabolite profiles
(5)
By using the smoothed experimental data, the kinetic parameters defined in Eqs. (2)–(5) were estimated. The two-step parameter-estimating strategy will be elaborated in the Results and Discussion section. Given these parameters and initial concentrations of glucose, yeast biomass, and ethanol, Eqs. (2), (4) and (5) were solved simultaneously. To evaluate the goodness-of-fit
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Table 1 Relationship among Pmax , So and ORP under redox potential-controlled VHG fermentation conditions. So (g/l)
300 ± 8.06 253 ± 3.77 203 ± 4.75
ORP (mV) No controla
−150
−100
118.67 130.17 140.51
127.46 136.02 150.25
135.59 153.46 159.51
a For VHG fermentation without redox potential control, the ORP value was taken by averaging redox potential readings that were below −150 mV.
were constructed to assist bioethanol producers to select the most suitable fermentation conditions when operating VHG ethanol fermentation process. 3.1. Estimation of growth-related kinetic parameters
Fig. 1. Rearranged experimental data taken from Ref. [15]. (a) Illustration of growth-association and nongrowth-association between yeast biomass and ethanol production. (b) Illustration of linear relationship between glucose consumption and ethanol production. Glucose feed: A, 300 ± 8.06 g/l; B, 253 ± 3.77 g/l; C, 203 ± 4.75 g/l. Redox potential level: a, no control; b, −150 mV; c, −100 mV. Glucose consumption −S = So − S, Ethanol production P = P − Po .
between experimental and modeled data, a simple R2 criterion was adopted and calculated by Eq. (6): R2 = 1 −
(m − mpred )2 2 ¯ (m − m)
(6)
3. Results and discussion Lin et al. [15] reported that redox potential profiles correlated to yeast growth patterns during VHG fermentation. Different redox potential levels and glucose feeds result in different fermentation efficiencies. To model the associated growth kinetics and to simulate the redox potential-controlled VHG fermentation, we first described the approaches used to estimate kinetic parameters relating to yeast growth, glucose consumption and ethanol production. We then illustrated the application of estimated growth parameters to predict profiles of yeast biomass, glucose, and ethanol under various combinations of redox potential levels and glucose feeds. Finally, three operating diagrams
When yeast is cultivated in a low concentration of glucose, it utilizes glucose rapidly and the biomass increases accordingly. Both the substrate inhibition constant (Ki ) and the maximum tolerable ethanol concentration (Pmax ) can be ignored; meaning that Eq. (2) can be simplified to become the Monod growth model. Using the double reciprocal method, one can graphically determine the maximum specific growth rate (max ) and the half saturation constant (Ks ). In contrast, all the kinetic parameters in Eq. (2) need to be taken into consideration when high glucose feed (i.e., >200 g/l in this study) is encountered. When only the first 6 h of measured glucose and biomass data were used, the ethanol concentration in the fermenter was about 15 g/l, which is below the inhibition level (ca. 40 g/l in this study). Hence, the product toxification term in Eq. (2) is neglected. Given the biomass distribution (i.e., dX/dt) and the glucose profile (S), the remaining growth kinetic parameters in Eq. (2) were determined (Table 2) by means of the global optimization technique (FMINSEARCH routine in Matlab). Keeping max , Ks , and Ki as constants, the full time-course profiles of glucose, biomass, and ethanol along with the full timecourse biomass distribution were used and incorporated into Eq. (2). The same global optimization technique was applied to each respective experimental setting (Table 1): glucose feed (So ) and redox potential level (ORP). As a result, the corresponding maximum tolerable ethanol concentration (Pmax ) and the degree of ethanol toxicity (˛) were estimated. The So , ORP, and Pmax were further related by means of linear regression (Eq. (3)) to obtain a fitted correlation. To simplify the expression of Eq. (2), all ˛ values were averaged to become a constant. All the above-noted parameters were compiled in Table 2. Note that Pmax is an indicator to the extent that yeast tolerates ethanol; the higher the Pmax value, the stronger the yeast resistance to ethanol toxicity. Propagating yeast under a high redox potenTable 2 Summary of estimated kinetic parameters for yeast growth, ethanol production, and glucose consumption under redox potential-controlled VHG conditions. Kinetic parameters for yeast growth max = 0.68 h−1 Ks = 0.213 g/l Ki = 386.64 g/l ˛ = 2.98 Pmax = −0.208So + 0.236ORP + 226 g/l Kinetic parameters for ethanol production k1 = 5.14 k2 = 0.034 1/h ˇ1 = 0.397 ˇ2 = 1.53 Kinetic parameters for glucose consumption YSP = 8.44 − 4.35 × 10−3 So + 9.16 × 10−5 So2 + 1.72 × 10−2 ORP + 5.86 × 10−5 ORP 2
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Fig. 2. Profiles of experimental data and simulated results. Glucose feed: A, 300 ± 8.06 g/l; B, 253 ± 3.77 g/l; C, 203 ± 4.75 g/l. Redox potential level: a, no control; b, −150 mV; c, −100 mV. Each experiment was conducted in duplicate.
tial environment favors the synthesis of unsaturated fatty acids by yeast, which are subsequently used as building blocks to construct their cell membranes [16]. A well-structured cell membrane protects the yeast, thus counteracting ethanol-induced stress. A high glucose feed results in a strong osmotic effect that reduces the yeast’s capability to combat ethanol tolerance since the intracellular metabolic flow is re-channeled to overcome osmotic stress. It is well known that the viability of S. cerevisiae decreased following an increase of osmotic pressure [17]. Therefore, VHG ethanol fermentation operated under low glucose feed and high redox potential level can enhance yeast’s tolerance to ethanol stress (Table 1). 3.2. Estimation of product-related kinetic parameters The product-related kinetic parameters defined in Eq. (4) were estimated by providing biomass (dX/dt) and ethanol (dP/dt) distribution data. All 18 experimental data were lumped to become one single data set and optimized by FIMSEARCH routine. Hence, two growth-associate parameters (k1 and ˇ1 ) and another two nongrowth-associated parameters (k2 and ˇ2 ) were found and listed in Table 2. 3.3. Estimation of substrate-related kinetic parameters A linear relationship between glucose consumption (−S) and ethanol production (P) was observed for all experimental data (Fig. 1b), and such a relationship is represented by a glucoseto-ethanol yield coefficient (YSP , Eq. (5)). During VHG ethanol
fermentation, the amount of ethanol produced is affected by the presence of glucose feed. In principle, the higher the glucose feed, the more ethanol will be produced. However, when the initial glucose concentration exceeds a threshold concentration, the glucose-induced osmotic stress slows down the fermentation rate. Additionally, controlling the redox potential indirectly alters the intracellular metabolic redistribution [18], consequently affecting ethanol productivity. Hence, we correlated YSP to be a function of glucose feed (So ) and redox potential level (ORP). Such a correlation is listed in Table 2, and the estimation procedure is described as follows. Given a set of S and P obtained under one particular So and ORP condition, the corresponding YSP was estimated by linear fitting technique. The above-noted procedure was repeated for all the remaining 17 experiments. Hence, a table of So , ORP, and YSP was constructed, and a two-parameter second-order polynomial fit was implemented to relate YSP to So and ORP. 3.4. Simulation and goodness of fit Kinetic parameters estimated from above were obtained by optimizing Eqs. (2), (4) and (5) individually. To evaluate the usefulness of these parameters when applied to VHG ethanol fermentation, we solved all three equations simultaneously by providing them with respective initial concentration of glucose, biomass, and ethanol along with the redox potential level pertaining to one of the 18 experiments. The simulation results are illustrated in Fig. 2. We used R2 (defined in Eq. (6)) as the criterion to evaluate the goodness of fit, and found that the R2 values of
C.-G. Liu et al. / Biochemical Engineering Journal 56 (2011) 63–68
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Fig. 4. Operating diagram illustrating the effect of glucose feed and redox potential level on the final ethanol concentration under redox potential-controlled VHG fermentation conditions.
Fig. 3. Operating diagram illustrating the effect of glucose feed and redox potential level on (a) the residual glucose, and (b) the fermentation duration under redox potential-controlled VHG fermentation conditions.
the predicted results are greater than 0.95. This indicates that the estimated kinetic parameters could be used in the current experimental settings to predict glucose, biomass and ethanol profiles. Note that the settings were: glucose, [200, 300 g/l]; redox potential level, [no control, −100 mV]; and the fermentation time up to 48 h. For the no control case, the measured redox potential readings below −150 mV were averaged and used during simulation.
one of the criteria when selecting VHG fermentation operating conditions. A low glucose feed and a high redox potential level result in a smaller amount of residual glucose (Fig. 3a) and a short fermentation time (Fig. 3b). When the glucose feed is greater than 250 g/l and the redox potential level was less than −120 mV, the presence of residual glucose was observed, indicating that such a combination of glucose feed and redox potential level is not a proper choice when operating VHG ethanol fermentation. Other than the residual glucose issue, the final ethanol concentration and fermentation efficiency are two additional criteria when choosing appropriate VHG fermentation operating conditions. Fig. 4 shows the predicted final ethanol concentration subjected to variations of glucose feed and redox potential level. This operating diagram demonstrates a monotonic increase in ethanol concentration until the glucose feed reaches 260 g/l, and any further increase in glucose feed results in an opposite outcome in conjunction with incomplete glucose utilization (Fig. 3a). The effect of redox potential level is also phenomenal. The best redox potential level ranges between −140 and −150 mV. The effect of glucose feed and redox potential level on the fermentation efficiency is shown in Fig. 5. When the glucose feed is greater than 280 g/l, the fermentation efficiency is always below 90%, irrespective of the redox potential level; whereas, the
3.5. Application of kinetic parameters and construction of operating diagrams To extend the use of estimated kinetic parameters and apply to select fermentation operating conditions towards high fermentation efficiency, which is defined as P/(−0.511S), three operating diagrams were thus constructed. To do so, we carried out several simulations with the following initial conditions: glucose, [200, 300 g/l]; biomass, 0.1 g/l; ethanol, 5 g/l; redox potential level, [−200, −100 mV]; and fermentation duration, 48 h. The fermentation duration refers to the total time required to complete one batch run. In this simulation, the maximal fermentation duration was constrained to 48 h to satisfy most current industrial operating condition. After VHG fermentation, the unspent glucose increases the operation difficulty and the cost of subsequent downstream processing, such as the separation of unconverted glucose, the delivery of ever-viscous fermentation broth during distillation. Therefore, the extent of glucose utilization (or the amount of residual glucose) is
Fig. 5. Operating diagram illustrating the effect of glucose feed and redox potential level on the fermentation efficiency under redox potential-controlled VHG fermentation conditions.
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influence of redox potential level on the fermentation efficiency becomes significant when the glucose feed was in a range of 210 and 270 g/l. In this range, the redox potential level can be varied from −190 to −110 mV. The fermentation efficiency greater than 94% can be attained when the glucose feed is held between 200 and 240 g/l. When the glucose feed and the redox potential level are kept at 235 g/l and −145 mV, the highest attainable fermentation efficiency is 97.2%. It has been examined that intracellular redox balance relates to energy metabolism and production of metabolites [19]. A high redox potential level implies that there is more dissolved oxygen available for yeast, which triggers the respiratory circuitry towards the TCA cycle, resulting in low fermentation efficiency. In other words, there is a lesser amount of carbon being channeled to reductive route for ethanol formation [15]. When the redox potential was set too low, the reduced fermentation environment induces the over-expression of GDP2 gene, which also lowers ethanol production [20]. 4. Conclusions We proposed a new semi-empirical growth kinetic model specific to the redox potential-controlled VHG ethanol fermentation process. The growth model took glucose feed and redox potential level into consideration. A two-step parameter-estimating strategy to estimate relevant kinetic parameters was described. Combining the growth model along with estimated ethanol and glucose kinetic parameters, we were able to simulate redox potential-controlled VHG ethanol fermentation processes with high accuracy. The simulated results were further applied to generate three operating diagrams, which could be used by the bioethanol producers to locate the best combination of glucose feed and redox potential level to operate high efficient and productive VHG ethanol fermentation process. References [1] K.C. Thomas, S.H. Hynes, W.M. Ingledew, Practical and theoretical considerations in the production of high concentrations of alcohol by fermentation, Process Biochem. 31 (1996) 321–331. [2] F.W. Bai, W.A. Anderson, M. Moo-Young, Ethanol fermentation technologies from sugar and starch feedstocks, Biotechnol. Adv. 26 (2008) 89–105.
[3] R. Devantier, B. Scheithauer, S.G. Villas-Bôas, S. Pedersen, L. Olsson, Metabolite profiling for analysis of yeast stress response during very high gravity ethanol fermentations, Biotechnol. Bioeng. 90 (2005) 703–714. [4] E. Rosenfeld, B. Beauvoit, B. Blondin, J.M. Salmon, Oxygen consumption by anaerobic Saccharomyces cerevisiae under enological conditions: effect on fermentation kinetics, Appl. Environ. Microbiol. 69 (2003) 113–121. [5] E. Oura, Effect of aeration intensity on the biochemical composition of baker’s yeast. I. Factors affecting the type of metabolism, Biotechnol. Bioeng. 16 (1974) 1197–1212. [6] E. Heinzle, J. Moes, M. Griot, E. Sandmeier, I.J. Dunn, R. Bucher, Measurement and control of dissolved oxygen below 100 ppb, Ann. N. Y. Acad. Sci. 469 (1986) 178–189. [7] L. Kjaergaard, The redox potential: its use and control in biotechnology, Adv. Biochem. Eng. 7 (1977) 131–150. [8] S.K. Dahod, Redox potential as a better substitute for dissolved oxygen in fermentation process control, Biotechnol. Bioeng. 24 (1982) 2123–2125. [9] D.C. Sheu, K.J. Duan, S.R. Jou, Y.C. Chen, C.W. Chen, Production of xylitol from Candida tropicalis by using an oxidation–reduction potential-stat controlled fermentation, Biotechnol. Lett. 25 (2003) 2065–2069. [10] W.F. Hu, S.N. Sin, H. Chua, P.H.F. Yu, Synthesis of polyhydroxyalkanoate (PHA) from excess activated sludge under various oxidation–reduction potentials (ORP) by using acetate and propionate as carbon sources, Appl. Biochem. Biotechnol. Part A 121 (2005) 289–301. [11] C. Du, H. Yan, Y. Zhang, Y. Li, Z. Cao, Use of oxidoreduction potential as an indicator to regulate 1, 3-propanediol fermentation by Klebsiella pneumoniae, Appl. Microbiol. Biotechnol. 69 (2006) 554–563. [12] M. Jiang, J. Li, K. Chen, Y. Wang, J. Ma, P. Wei, Effect of redox potential regulation on the succinic acid production by anaerobic fermentation of Actinobacillus succinogenes, Chem. Ind. Eng. Progress (China) 27 (2008) 1250–1253. [13] A. Mulchandani, J.H.T. Luong, Microbial inhibition kinetics revisited, Enzyme Microb. Technol. 11 (1989) 66–73. [14] S. Aiba, M. Shoda, M. Nagatani, Kinetics of product inhibition in alcohol fermentation, Biotechnol. Bioeng. 10 (1968) 845–864. [15] Y.-H. Lin, W.S. Chien, K.J. Duan, Correlations between reduction–oxidation potential profiles and growth patterns of Saccharomyces cerevisiae during veryhigh-gravity fermentation, Process Biochem. 45 (2010) 765–770. [16] C. Fornairon-Bonnefond, V. Demaretz, E. Rosenfeld, J.M. Salmon, Oxygen addition and sterol synthesis in Saccharomyces cerevisiae during enological fermentation, J. Biosci. Bioeng. 93 (2002) 176–182. [17] A.K. Adya, E. Canetta, G.M. Walker, Atomic force microscopic study of the influence of physical stresses on Saccharomyces cerevisiae and Schizosaccharomyces pombe, FEMS Yeast Res. 6 (2006) 120–128. [18] S. Heux, J.-M. Sablayrolles, R. Cachon, S. Dequin, Engineering a Saccharomyces cerevisiae wine yeast that exhibits reduced ethanol production during fermentation under controlled microoxygenation conditions, Appl. Environ. Microbiol. 72 (2006) 5822–5828. [19] P. Johannes, W. van Dijken, S. Alexander, Redox balances in the metabolism of sugars by yeasts, FEMS Microbiol. Lett. 32 (1986) 199–224. [20] R. Ansell, K. Granath, S. Hohmann, J.M. Thevelein, L. Adler, The two isoenzymes for yeast NAD+ -dependent glycerol 3-phosphate dehydrogenase encoded by GPD1 and GPD2 have distinct roles in osmoadaptation and redox regulation, EMBO J. 16 (1997) 2179–2187.
Contents lists available at ScienceDirect
Biochemical Engineering Journal journal homepage: www.elsevier.com/locate/bej
A kinetic growth model for Saccharomyces cerevisiae grown under redox potential-controlled very-high-gravity environment Chen-Guang Liu a , Yen-Han Lin b,∗ , Feng-Wu Bai a a b
School of Bioscience and Bioengineering, Dalian University of Technology, Dalian, Liaoning 116023, China Department of Chemical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, SK S7N5A9, Canada
a r t i c l e
i n f o
Article history: Received 24 December 2010 Received in revised form 29 March 2011 Accepted 14 May 2011 Available online 23 May 2011 Keywords: Saccharomyces cerevisiae Ethanol Kinetic models Very-high-gravity fermentation Redox potential Operating diagram
a b s t r a c t A growth kinetic model for redox potential-controlled very-high-gravity (VHG) fermentation was developed. The model is semi-empirical and two important VHG fermentation operating conditions including glucose feed and redox potential level were incorporated in the model. The model consists of a substrate inhibition term and a product toxification term. A two-step parameter-estimating strategy was proposed and implemented. In the first step, the first few experimentally collected data points were used to estimate parameters relating to the substrate inhibition term; in the second step, the complete data set was used to estimate parameters relating to the product toxification term. The developed growth model could fit the original data with an R2 value >0.95. Three operating diagrams were constructed by using the results generated from the developed model. Each respective diagram could be used to select the best operating condition for the shortest fermentation time, the highest final ethanol concentration, or the highest fermentation efficiency. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Fuel alcohol is the most widely used petroleum-based fuel alternative nowadays. It is mainly applied to the transportation sector to reduce carbon dioxide emission, and is regarded as an environmentally friendly and sustainable fuel substitute due to its net-zero carbon discharge. Fuel alcohol is produced by Saccharomyces cerevisiae in fermentation with the consumption of grain-based crops or sugar canes. Ethanol is the primary metabolite secreted by yeast; the more sugar present during fermentation, the more ethanol produced. Very-high-gravity (VHG) fermentation is a technology where the fermenter is over-supplemented by glucose for ethanol production. The typical species used for this purpose is ethanol-tolerating S. cerevisiae. Hence, high ethanol productivity and significant energy savings can be realized [1,2]. During the course of VHG ethanol fermentation, yeast simultaneously encounters physical, chemical, and biological stresses [3]. Particularly, in the late stage of stationary phase, abrupt cell death attributed to the accumulated ethanol in the fermenter is commonly observed, and consequently prolongs the fermentation time. One approach to combat the ethanol toxicity during batch fermentation is to provide oxygen
∗ Corresponding author. Tel.: +1 306 966 4764; fax: +1 306 966 4777. E-mail address: [email protected] (Y.-H. Lin). 1369-703X/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.bej.2011.05.008
for yeast to enhance yeast activity [4]. On the other hand, an over-aerated fermenter may alter intracellular metabolic pathways, leading to low ethanol production [5]. Measuring dissolved oxygen at low levels in a large fermenter is a challenge [6]. One of the reliable and practical alternatives is the redox potential measurement [7,8]. The redox potential is an indicator of the net balance of overall reduction and oxidation in a solution. A high redox potential level signifies a high tendency of losing electrons or the presence of a high level of dissolved oxygen, and/or vice versa. The application of redox potential to cultivate organisms at different micro-aerobic environments has been reported [9–12]. To model yeast growth kinetics under VHG fermentation, one requires an understanding of substrate osmosis resulting from high glucose feed which later results in the buildup of ethanol that inhibits and adversely toxifies yeast, thus causing the growth arrest. Due to the hidden biological complexity under VHG conditions, the common growth models were not applicable [13,14]; specifically, when the redox potential was implemented to modulate reduction–oxidation balance within yeast. In this study, we developed a new semi-empirical growth kinetic model that purposefully took glucose feeds and redox potential levels into consideration. Based on experimental observations [15], a two-step parameterestimating strategy was proposed and implemented to estimate kinetic parameters pertinent to yeast growth, ethanol production, and glucose consumption. Accordingly, operating diagrams were
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C.-G. Liu et al. / Biochemical Engineering Journal 56 (2011) 63–68
Nomenclature a0 , a1 , a2 k1 k2 Ki Ks m ˆ m ¯ m mpred ORP P Po Pmax r
S So t X YSP
regression coefficients defined in Eq. (3) growth-associated parameter (g/l/h) nongrowth-associated parameter (g/l/h) glucose inhibition constant (g/l) half saturation constant (g/l) metabolite concentration (g/l) maximum metabolite concentration (g/l) average metabolite concentration (g/l) predicted metabolite concentration (g/l) redox potential level (mV) ethanol concentration at time t (g/l) ethanol concentration at time 0 (g/l) maximum tolerable ethanol concentration (g/l) positive, maximum specific metabolite production rate (1/h); negative, maximum specific metabolite consumption rate (1/h) glucose concentration at time t (g/l) glucose feed or initial glucose concentration (g/l) time (h) biomass concentration (g/l) yield of glucose to ethanol (g/g)
Greek letters ˛ degree of ethanol toxicity order of growth association ˇ1 ˇ2 order of nongrowth association P ethanol production (g/l) −S glucose consumption (g/l) specific growth rate (1/h) max maximum specific growth rate (1/h)
constructed to assist the fuel alcohol industry to locate the most suitable operating conditions for VHG ethanol fermentation process.
2. Materials and methods 2.1. Strain, growth media, fermentation, and sample analysis Strain, growth media, and sample analysis were previously reported [15]. Briefly, an industrial S. cerevisiae strain (Ethanol RedTM ) was pre-cultured overnight and cultivated in a jar fermenter. In addition to 300 ± 8.06, 253 ± 3.77, or 203 ± 4.75 g glucose/l, the growth medium consisted of trace mineral salts, vitamin cocktail, urea, yeast extract, and sodium glutamate. The fermentation broth was collected every 6 h, and the violet red staining technique was implemented to differentiate viable and dead cells. As a result, cell viability was estimated. By using HPLC, the supernatant portion of the broth was used to quantify the residual glucose, ethanol, and other metabolites.
collected from batch redox potential-controlled VHG fermentation. The curve is expressed as
m dm =r 1− dt ˆ m
m
(1)
When the r value is positive, it is called the maximum specific metabolite production rate; when negative, it is called the maximum specific metabolite consumption rate. We used our previously reported data [15] as raw data and smoothed it by the above-noted logistic growth curve. VHG fermentation characterizes high glucose feed where substrate-induced osmotic stress is observed, leading to a long lag phase. To simulate this phenomenon, a substrate inhibition model (the first term on the right hand side of Eq. (2)) was adopted. As fermentation continues, the buildup of ethanol inhibits and later toxifies yeast propagation, resulting in drastic reduction in yeast viability. To simulate such an adverse effect on a yeast population, a product toxification model (the second term on the right hand side of Eq. (2)) was incorporated and shown below: = max =0
S P 1− Pmax S + KS + S 2 /Ki
˛ when P < Pmax
(2)
when P > Pmax
Refer to Fig. 2 as reported in [15], the glucose utilization rate correlates to the glucose feed; that is, the lower the glucose feed (So ), the faster the fermentation rate is attainable. Further refer to Fig. 3 in [15], it illustrates that the yeast viability can be modulated by varying redox potential levels (ORP). It is known that ethanol synthesis by yeast is classified as primary fermentation, meaning that the higher the viable population, the more ethanol would be expected. As a result, a higher final ethanol concentration could be obtained. The final ethanol concentration refers to ethanol obtained at the completion of fermentation. Hence, a linear relationship among the glucose feed, the redox potential level, and the maximum ethanol concentration was proposed and expressed as follows: Pmax = a0 + a1 S0 + a2 ORP
(3)
Refer to Fig. 1a, the amount of ethanol produced is directly associated with the population size of yeast. When the biomass concentration is greater than 7.4 g/l (see dotted line shown in Fig. 1a, the yeast growth slows down and nearly stops, and the ethanol continues to accumulate. Based on these observations, we proposed Eq. (4) to describe yeast growth kinetics:
dX dP = k1 dt dt
ˇ1
+ k2 X ˇ2
(4)
The first two terms on the right-hand side of Eq. (4) represent growth-associated and non-growth-associated ethanol production, respectively. While plotting the change of ethanol (P) versus the change of glucose (−S), a linear relationship is observed (Fig. 1b). Accordingly, a yield coefficient (YSP ) was defined and presented in Eq. (5):
2.2. Data processing and modeling −S = YSP P Experimentally collected data are typically discrete. However when applied to numerical predictions directly, a significant discrepancy between actual and predicted data points occurs. Hence, the data smoothing approach is necessary before conducting numerical calculations. There are many sigmoidal equations available to conduct data smoothing. In this study, we chose a three-parameter logistic growth curve to model metabolite profiles
(5)
By using the smoothed experimental data, the kinetic parameters defined in Eqs. (2)–(5) were estimated. The two-step parameter-estimating strategy will be elaborated in the Results and Discussion section. Given these parameters and initial concentrations of glucose, yeast biomass, and ethanol, Eqs. (2), (4) and (5) were solved simultaneously. To evaluate the goodness-of-fit
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Table 1 Relationship among Pmax , So and ORP under redox potential-controlled VHG fermentation conditions. So (g/l)
300 ± 8.06 253 ± 3.77 203 ± 4.75
ORP (mV) No controla
−150
−100
118.67 130.17 140.51
127.46 136.02 150.25
135.59 153.46 159.51
a For VHG fermentation without redox potential control, the ORP value was taken by averaging redox potential readings that were below −150 mV.
were constructed to assist bioethanol producers to select the most suitable fermentation conditions when operating VHG ethanol fermentation process. 3.1. Estimation of growth-related kinetic parameters
Fig. 1. Rearranged experimental data taken from Ref. [15]. (a) Illustration of growth-association and nongrowth-association between yeast biomass and ethanol production. (b) Illustration of linear relationship between glucose consumption and ethanol production. Glucose feed: A, 300 ± 8.06 g/l; B, 253 ± 3.77 g/l; C, 203 ± 4.75 g/l. Redox potential level: a, no control; b, −150 mV; c, −100 mV. Glucose consumption −S = So − S, Ethanol production P = P − Po .
between experimental and modeled data, a simple R2 criterion was adopted and calculated by Eq. (6): R2 = 1 −
(m − mpred )2 2 ¯ (m − m)
(6)
3. Results and discussion Lin et al. [15] reported that redox potential profiles correlated to yeast growth patterns during VHG fermentation. Different redox potential levels and glucose feeds result in different fermentation efficiencies. To model the associated growth kinetics and to simulate the redox potential-controlled VHG fermentation, we first described the approaches used to estimate kinetic parameters relating to yeast growth, glucose consumption and ethanol production. We then illustrated the application of estimated growth parameters to predict profiles of yeast biomass, glucose, and ethanol under various combinations of redox potential levels and glucose feeds. Finally, three operating diagrams
When yeast is cultivated in a low concentration of glucose, it utilizes glucose rapidly and the biomass increases accordingly. Both the substrate inhibition constant (Ki ) and the maximum tolerable ethanol concentration (Pmax ) can be ignored; meaning that Eq. (2) can be simplified to become the Monod growth model. Using the double reciprocal method, one can graphically determine the maximum specific growth rate (max ) and the half saturation constant (Ks ). In contrast, all the kinetic parameters in Eq. (2) need to be taken into consideration when high glucose feed (i.e., >200 g/l in this study) is encountered. When only the first 6 h of measured glucose and biomass data were used, the ethanol concentration in the fermenter was about 15 g/l, which is below the inhibition level (ca. 40 g/l in this study). Hence, the product toxification term in Eq. (2) is neglected. Given the biomass distribution (i.e., dX/dt) and the glucose profile (S), the remaining growth kinetic parameters in Eq. (2) were determined (Table 2) by means of the global optimization technique (FMINSEARCH routine in Matlab). Keeping max , Ks , and Ki as constants, the full time-course profiles of glucose, biomass, and ethanol along with the full timecourse biomass distribution were used and incorporated into Eq. (2). The same global optimization technique was applied to each respective experimental setting (Table 1): glucose feed (So ) and redox potential level (ORP). As a result, the corresponding maximum tolerable ethanol concentration (Pmax ) and the degree of ethanol toxicity (˛) were estimated. The So , ORP, and Pmax were further related by means of linear regression (Eq. (3)) to obtain a fitted correlation. To simplify the expression of Eq. (2), all ˛ values were averaged to become a constant. All the above-noted parameters were compiled in Table 2. Note that Pmax is an indicator to the extent that yeast tolerates ethanol; the higher the Pmax value, the stronger the yeast resistance to ethanol toxicity. Propagating yeast under a high redox potenTable 2 Summary of estimated kinetic parameters for yeast growth, ethanol production, and glucose consumption under redox potential-controlled VHG conditions. Kinetic parameters for yeast growth max = 0.68 h−1 Ks = 0.213 g/l Ki = 386.64 g/l ˛ = 2.98 Pmax = −0.208So + 0.236ORP + 226 g/l Kinetic parameters for ethanol production k1 = 5.14 k2 = 0.034 1/h ˇ1 = 0.397 ˇ2 = 1.53 Kinetic parameters for glucose consumption YSP = 8.44 − 4.35 × 10−3 So + 9.16 × 10−5 So2 + 1.72 × 10−2 ORP + 5.86 × 10−5 ORP 2
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Fig. 2. Profiles of experimental data and simulated results. Glucose feed: A, 300 ± 8.06 g/l; B, 253 ± 3.77 g/l; C, 203 ± 4.75 g/l. Redox potential level: a, no control; b, −150 mV; c, −100 mV. Each experiment was conducted in duplicate.
tial environment favors the synthesis of unsaturated fatty acids by yeast, which are subsequently used as building blocks to construct their cell membranes [16]. A well-structured cell membrane protects the yeast, thus counteracting ethanol-induced stress. A high glucose feed results in a strong osmotic effect that reduces the yeast’s capability to combat ethanol tolerance since the intracellular metabolic flow is re-channeled to overcome osmotic stress. It is well known that the viability of S. cerevisiae decreased following an increase of osmotic pressure [17]. Therefore, VHG ethanol fermentation operated under low glucose feed and high redox potential level can enhance yeast’s tolerance to ethanol stress (Table 1). 3.2. Estimation of product-related kinetic parameters The product-related kinetic parameters defined in Eq. (4) were estimated by providing biomass (dX/dt) and ethanol (dP/dt) distribution data. All 18 experimental data were lumped to become one single data set and optimized by FIMSEARCH routine. Hence, two growth-associate parameters (k1 and ˇ1 ) and another two nongrowth-associated parameters (k2 and ˇ2 ) were found and listed in Table 2. 3.3. Estimation of substrate-related kinetic parameters A linear relationship between glucose consumption (−S) and ethanol production (P) was observed for all experimental data (Fig. 1b), and such a relationship is represented by a glucoseto-ethanol yield coefficient (YSP , Eq. (5)). During VHG ethanol
fermentation, the amount of ethanol produced is affected by the presence of glucose feed. In principle, the higher the glucose feed, the more ethanol will be produced. However, when the initial glucose concentration exceeds a threshold concentration, the glucose-induced osmotic stress slows down the fermentation rate. Additionally, controlling the redox potential indirectly alters the intracellular metabolic redistribution [18], consequently affecting ethanol productivity. Hence, we correlated YSP to be a function of glucose feed (So ) and redox potential level (ORP). Such a correlation is listed in Table 2, and the estimation procedure is described as follows. Given a set of S and P obtained under one particular So and ORP condition, the corresponding YSP was estimated by linear fitting technique. The above-noted procedure was repeated for all the remaining 17 experiments. Hence, a table of So , ORP, and YSP was constructed, and a two-parameter second-order polynomial fit was implemented to relate YSP to So and ORP. 3.4. Simulation and goodness of fit Kinetic parameters estimated from above were obtained by optimizing Eqs. (2), (4) and (5) individually. To evaluate the usefulness of these parameters when applied to VHG ethanol fermentation, we solved all three equations simultaneously by providing them with respective initial concentration of glucose, biomass, and ethanol along with the redox potential level pertaining to one of the 18 experiments. The simulation results are illustrated in Fig. 2. We used R2 (defined in Eq. (6)) as the criterion to evaluate the goodness of fit, and found that the R2 values of
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Fig. 4. Operating diagram illustrating the effect of glucose feed and redox potential level on the final ethanol concentration under redox potential-controlled VHG fermentation conditions.
Fig. 3. Operating diagram illustrating the effect of glucose feed and redox potential level on (a) the residual glucose, and (b) the fermentation duration under redox potential-controlled VHG fermentation conditions.
the predicted results are greater than 0.95. This indicates that the estimated kinetic parameters could be used in the current experimental settings to predict glucose, biomass and ethanol profiles. Note that the settings were: glucose, [200, 300 g/l]; redox potential level, [no control, −100 mV]; and the fermentation time up to 48 h. For the no control case, the measured redox potential readings below −150 mV were averaged and used during simulation.
one of the criteria when selecting VHG fermentation operating conditions. A low glucose feed and a high redox potential level result in a smaller amount of residual glucose (Fig. 3a) and a short fermentation time (Fig. 3b). When the glucose feed is greater than 250 g/l and the redox potential level was less than −120 mV, the presence of residual glucose was observed, indicating that such a combination of glucose feed and redox potential level is not a proper choice when operating VHG ethanol fermentation. Other than the residual glucose issue, the final ethanol concentration and fermentation efficiency are two additional criteria when choosing appropriate VHG fermentation operating conditions. Fig. 4 shows the predicted final ethanol concentration subjected to variations of glucose feed and redox potential level. This operating diagram demonstrates a monotonic increase in ethanol concentration until the glucose feed reaches 260 g/l, and any further increase in glucose feed results in an opposite outcome in conjunction with incomplete glucose utilization (Fig. 3a). The effect of redox potential level is also phenomenal. The best redox potential level ranges between −140 and −150 mV. The effect of glucose feed and redox potential level on the fermentation efficiency is shown in Fig. 5. When the glucose feed is greater than 280 g/l, the fermentation efficiency is always below 90%, irrespective of the redox potential level; whereas, the
3.5. Application of kinetic parameters and construction of operating diagrams To extend the use of estimated kinetic parameters and apply to select fermentation operating conditions towards high fermentation efficiency, which is defined as P/(−0.511S), three operating diagrams were thus constructed. To do so, we carried out several simulations with the following initial conditions: glucose, [200, 300 g/l]; biomass, 0.1 g/l; ethanol, 5 g/l; redox potential level, [−200, −100 mV]; and fermentation duration, 48 h. The fermentation duration refers to the total time required to complete one batch run. In this simulation, the maximal fermentation duration was constrained to 48 h to satisfy most current industrial operating condition. After VHG fermentation, the unspent glucose increases the operation difficulty and the cost of subsequent downstream processing, such as the separation of unconverted glucose, the delivery of ever-viscous fermentation broth during distillation. Therefore, the extent of glucose utilization (or the amount of residual glucose) is
Fig. 5. Operating diagram illustrating the effect of glucose feed and redox potential level on the fermentation efficiency under redox potential-controlled VHG fermentation conditions.
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influence of redox potential level on the fermentation efficiency becomes significant when the glucose feed was in a range of 210 and 270 g/l. In this range, the redox potential level can be varied from −190 to −110 mV. The fermentation efficiency greater than 94% can be attained when the glucose feed is held between 200 and 240 g/l. When the glucose feed and the redox potential level are kept at 235 g/l and −145 mV, the highest attainable fermentation efficiency is 97.2%. It has been examined that intracellular redox balance relates to energy metabolism and production of metabolites [19]. A high redox potential level implies that there is more dissolved oxygen available for yeast, which triggers the respiratory circuitry towards the TCA cycle, resulting in low fermentation efficiency. In other words, there is a lesser amount of carbon being channeled to reductive route for ethanol formation [15]. When the redox potential was set too low, the reduced fermentation environment induces the over-expression of GDP2 gene, which also lowers ethanol production [20]. 4. Conclusions We proposed a new semi-empirical growth kinetic model specific to the redox potential-controlled VHG ethanol fermentation process. The growth model took glucose feed and redox potential level into consideration. A two-step parameter-estimating strategy to estimate relevant kinetic parameters was described. Combining the growth model along with estimated ethanol and glucose kinetic parameters, we were able to simulate redox potential-controlled VHG ethanol fermentation processes with high accuracy. The simulated results were further applied to generate three operating diagrams, which could be used by the bioethanol producers to locate the best combination of glucose feed and redox potential level to operate high efficient and productive VHG ethanol fermentation process. References [1] K.C. Thomas, S.H. Hynes, W.M. Ingledew, Practical and theoretical considerations in the production of high concentrations of alcohol by fermentation, Process Biochem. 31 (1996) 321–331. [2] F.W. Bai, W.A. Anderson, M. Moo-Young, Ethanol fermentation technologies from sugar and starch feedstocks, Biotechnol. Adv. 26 (2008) 89–105.
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