A. Vrsalović Presečki, Đ. Vasić-Rački: Modelling of the alcohol dehydrogenase production in baker's yeast
Modelling of the alcohol dehydrogenase production in baker's yeast
Ana Vrsalović Presečki, Đurđa Vasić-Rački
Faculty of Chemical Engineering and Technology, University of Zagreb, Marulićev trg 19, HR-10000 Zagreb, Croatia, Phone: +385 (1) 4597-132, Fax: +385 (1) 4597-133, e-mail:
Baker's yeast was cultivated in batch bioreactor at different initial concentration of glucose and different oxygen feeding rate. Two baker's yeast cultivations with the initial glucose concentration of 30 g dm-3 and under micro-aerobic conditions (DO = 10 %) were carried out for the model development. The unstructured model was chosen for describing kinetic of baker's yeast growth and consumption of substrate. Growth associated production of ADH was observed. Model parameters were estimated using nonlinear regression by package program SCIENTIST. Comparing the results of simulation that were done by using does estimated parameters, and the experimental results, statistical model evaluation was done. Model is validated for different initial glucose concentrations under micro-aerobic (DO = 10 %) and aerobic conditions (DO = 40 %). By model validation is shown that mathematical model is valid for the cultivations under micro-aerobic conditions with the initial glucose concentration between 5 – 50 g dm-3. Under aerobic conditions proposed model is valid for describing biomass production, glucose consumption and change of ethanol concentration during the experiment. A lower volume activity of enzyme ADH in relation to the assigned biomass concentration, under aerobic conditions, was observed.
Introduction
Biotransformation has often been used for the production of chemical during the past century. There are two biotransformation systems; whole cells or isolated enzymes that are used as chemical catalyst and both display some advantages.
From the economical point of view, baker's yeast as a source of enzymes is very popular because1 it is very cheap and simple to use. It can be grown on simple, defined media, without any extraordinary requirements for the nutrients. Also baker's yeast is quite tolerant to changes of environmental conditions, i.e. its permissive ranges for physical and chemical parameters are very broad.
Metabolic growth of baker’s yeast, Saccharomyces cerevisae, is changed due to dissolved oxygen concentration and carbon source2,3. One of the products of the baker’s yeast metabolism is alcohol dehydrogenase (ADH). ADH belongs to oxydoreductases. The isolated enzyme has a molecular weight of about 1500004, quaternary structure stabilised by Zn-ions. Therefore, it belongs to a methaloenzyme group. It is dependent of the coenzyme nicotinamide adenine dinucleotide, which is involved, in two-electrons oxidation or reductions. ADH oxidises all primary alcohols and aldehydes (e.g. acetaldehyde and glyceraldehyde). Its activity decreases with the increase in a substrate chain length. ADH is the first enzyme that has been used to show that the transfer of hydrogen catalysed by dehydrogenase is stereo specific without influence of solvent. Enzyme ADH is used for preparation of chiral aldehydes by primary alcohols oxidation. Very large number of -hydroxyl and -amino alcohol can be oxidised in a corresponding aldehydes and also S- and R- amino alcohols can be oxidised in the aminoaldehydes5. The production of this enzyme by baker's yeast is directly depended to the conditions of cultivation. The oxidative and the reductive metabolisms of baker's yeast go through different biological pathways, i.e. different enzymes are used in these two metabolisms. The enzyme alcohol dehydrogenase is used only in the reductive metabolism for the oxidation of ethanol to acetaldehyde and the yeast cell serves to increase the activity of the alcohol dehydrogenase. If during the growth of the cell prevails the oxidative metabolism, the cell does not use the enzyme alcohol dehydrogenase, therefore the cell decreases its activity. Depending on the concentration of oxygen in the medium, both metabolisms take place in different relationship. Therefore optimising of these conditions and developing a model to describe the production of ADH was the aim of this work.
Experimental part
A pure culture of Saccharomyces cerevisiae cells was stored in the plates containing malt agar at the +4 °C. The culture was reactivated by inoculating a Saccharomyces cerevisiae cells from the solid substrate into an Erlenmeyer flask with 100 mL medium, which was incubated at 30 °C on a rotary shakers for 24 h.
The fermentation and shake flasks medium6 for experiment contained: FeSO4 7H2O 0.012 g dm-3, (NH4)2SO4 7.5 g dm-3, CaCl2 0.03 g dm-3, CuSO4 5H2O 0.001 g dm-3, KH2PO4 1.5 g dm-3, ZnSO4 7H2O 0.006 g dm-3 and MgSO4 7H2O 0.691 g dm-3 in distilled water. As a carbon source, different initial concentrations of glucose were used (cGO = 5, 10, 30, 50 g dm-3). Shake flask growth medium contained 10 g dm-3 glucose.
The batch growth of the baker’s yeast was carried out in a 5 dm3 reactor (Drasler, Slovenia) containing 3.5 dm3 medium. The bioreactor was equipped with standard control units for pH, temperature, aeration and stirrer speed. Computer acquisition to collect and monitor DO (dissolved oxygen) data every 10 s. was established. All fermentations were carried out at the temperature of 30 C. Dissolved oxygen concentration was kept about 10 % (micro-aerobic conditions) and about 40 % (aerobic conditions) concentration of saturation by variation of stirring (200 - 700 RPM) and air-flow rate (3 – 10 dm3 min-1). The fermentation medium and the bioreactor were sterilised at 120 C, except glucose, which was sterilised at 110 C.
A biomass wet weight change was monitored on the spectrophotometer at the wavelength 660 nm7 with a calibration curve. Changes in ethanol concentration and ADH activity were measured by the BOEHRINGER test8. The test sample for ADH activity was prepared by permeabilization the yeast cells with cetyltrimethylammonium bromide9. Glucose concentration was measured by standard colorenzymatic method (PAP). Oxygen concentration was calculated according to the correlation:
(1)
where cO,S represents saturation oxygen concentration (cO,S = 0.00712 g dm-3, calculated according to the Henry’s law) that was assumed to be constant during the experiment10.
The model parameters were estimated by non-linear regression analysis using the Nelder-Mead method11. The numerical values of the parameters were evaluated by fitting the model to the experimental data with the "Scientist"12 software. The model equations were solved numerically by the fourth order Runge-Kutta algorithm, which is also offered in the same software. The set of optimum parameters was used for the simulation.
The calculated data were compared with the experimental data, recalculated in the optimization routine and fed again to the integration step until minimal error between experimental and integrated values was achieved (built-in Scientist). The residual sum of squares was defined as the sum of the squares of the differences between experimental (yi) and calculated data (yi,calc).
Results and discussion
The yeast grown on glucose has two metabolisms; the oxidative and the reductive. The oxidative metabolism prevails when the supply of oxygen is high enough to oxidise pyruvate by the citric acid circle13. When the oxygen supply is not sufficient, pyruvate accumulates in the yeast cells because of their disability to oxidise it. The accumulation of pyruvate is connected with the formation of reductive equivalents (i.e. NADH) in later stages of the glycolysis. In that case the yeast cells reduce pyruvate to ethanol with the reoxidation of NADH to NAD at the same time. The oxidative and the reductive metabolisms go through different biological pathways, i.e. different enzymes are used in these two metabolisms. The enzyme alcohol dehydrogenase is used only in the reductive metabolism and the yeast cell serves to increase the activity of the alcohol dehydrogenase. If during the growth of the cell prevails the oxidative metabolism, the cell does not use the enzyme alcohol dehydrogenase, therefore the cell decreases its activity. Depending on the concentration of oxygen in the medium, both metabolisms take place in different relationship and so the enzyme alcohol dehydrogenase is not entirely deactivated in the yeast cells during the oxidative metabolism on glucose, but has a decreased activity. Therefore it was assumed that under micro-aerobic conditions (concentration of oxygen was kept constant between 10 – 20 %) yeast alcohol dehydrogenase activity would be maximal.
Model development
Two baker's yeast cultivations with the initial glucose concentration of 30 g dm-3 and under micro-aerobic conditions were carried out for the model development. Proposed model is based on the following assumptions10:
- reactor contains two phases (gas-liquid system), microorganisms are not considered as a separate phase because of their small size and water-like density
- the reactor contents are considered homogenous in axial and radial directions
- energy balance were not considered since effective temperature control was accomplished
- the mass transfer between gas and liquid phase is explained by film model which is also incorporated into the process model
In order to describe the change of the enzyme activity of the enzyme alcohol dehydrogenase the following two assumptions were introduced:
- enzyme production is following the biomass growth, i.e. enzyme production is growth associated14
- the enzyme deactivation caused by inappropriate conditions in a bioreactor (temperature, pH) can be described by the first order kinetic15
From these assumptions balance equations for biomass, glucose, ethanol oxygen and volume activity of the enzyme ADH for the batch reactor was derived:
(2)
(3)
(4)
(5)
(6)
In expressions 1, 2, 3, 4 and 5 left sides of equations present the accumulation of substance in time.
The biomass growth is an autocatalytic reaction expressed as:
(7)
and the total specific biomass growth rate is the sum of particular growth rate in different metabolisms:
(8)
i.e.
(9)
The glucose uptake rate follows the Michaelis-Menten kinetics:
(10)
However, glucose could be utilised through two metabolic pathways; the oxidative and the reductive. The oxidative metabolic pathway depends on the availability of the dissolved oxygen in the reaction medium, and therefore the quantity of glucose that can be utilised, oxidatively corresponds to the oxidative capacity, the rate of which can be expressed as follows:
(11)
From these two equations the rate of glucose utilisation in the oxidative metabolic pathway can be written as:
(12)
and the rest of glucose is utilised by the reductive metabolic pathway:
(13)
As the ethanol is formed by reductive pathway of glucose specific rate of ethanol production is given by:
(14)
The ethanol consumption follows the Michaelis-Menten kinetics, and it depends on the availability of dissolved oxygen as well. However, the consumption of ethanol could proceed only in the oxidative metabolic pathway. Yeast has an emphasised priority toward glucose, so that ethanol will not metabolise as long as measurable quantities of glucose can be found in the reaction medium. The mathematical description of the ethanol uptake rate is given by the following equations:
(15)
(16)
Oxygen consumption is given by the following equation:
(16)
For the parameter estimation initial values of all parameters that are used to describe baker’s yeast growth except parameter a and b were taken from the literature for the similar processes10,16. The initial values for the parameters YX/Et, , , YEt/G were approximately determined from the experimental results. The Michaelis-Menten parameters for the ethanol uptake (rEt,max, KEt) and for the limited oxygen respiration(rO,max, KO) and glucose constant of the saturation (KG) were taken from the literature10,16 considering the assumption that the dry cell weight is 30% of wet biomasss (Table 1a). Parameter a was assessed from the maximal specific activity (U of ADH / g of wet biomass). Parameters like maximum specific glucose consumption rate (rG,max), yields of oxygen on glucose and ethanol (YO/Et, YO/G) and parameter b for the enzyme deactivation were estimated by using the least square method to minimize difference between experimental and calculated values of state variables (confidence was set at 95 %). The list of parameters from the literature along with the evaluated one (together with the confidence intervals) is given in the table 1b. Confidence intervals of almost all parameters are less than 10% except the yield of oxygen on ethanol (YO/Et) that is responsible for the ethanol uptake rate.
Table 1.Parameters of the mathematical model: (a) from the literature, (b) estimated in this work
a)
Parameter / Literature values10,16rO,max [h-1] / 0.0384
rEt,max [h-1] / 0.07176
KG [g dm-3] / 0.612
KO [g dm-3] / 9.6·10-5
KEt [g dm-3] / 0.1012
b)
Parameter
/ Estimate values / Literature values10,16rG,max [h-1] / 0.212 0.0124 / 0.8856
YX/Et [gWW g-1] / 0.293 0.0131 / 0.7173
YO/Et [g g-1] / 2.838 0.5955 / 0.8904
YEt/G [g g-1] / 0.049 0.0051 / 0.4856
YO/G [g g-1] / 0.515 0.0676 / 0.3858
[gWW g-1] / 1.521 0.3662 / 1.6898
[gWW g-1] / 1.051 0.0691 / 0.1667
a [U gWW-1] / 0.400 0.0532 / -
b [h-1] / 0.015 0.0014 / -
The results of comparison model and experiment are presented in Figure 1. Biomass growth can be divided into two phases (Figure 1b): exponential phase and linear phase. During the exponential phase baker's yeast growth glucose is consumed aerobically and anaerobically as well. Anaerobic conditions are present only when the respiratory is insufficient to metabolise all sugar consumption aerobically. Ethanol is accumulated during the yeast growth under anaerobic conditions (Figure 1c) by reducing the acetaldehyde with the enzyme alcohol dehydrogenase. Therefore the volume activity of ADH increases as well (Figure 1d). The cause of slight decrease of volume activity is enzyme deactivation. Whereas the model results are placed within a standard deviation of experimental results it has been concluded that the proposed model shows good fitting with this cultivation.
Figure 1. Glucose (a), biomass wet weight (b), ethanol (c), volume activity (d) and dissolved oxygen (e) (cG0 30 g dm-3, micro-aerobic conditions – DO = 10 %) changes with time. experiment 1, experiment 2, ∙∙∙∙∙ mean of the experiment 1 and 2, — model, interval of one standard deviations of the experimental results.
As it could be seen from the results of simulations volume activity follows biomass growth, and with higher biomass concentration higher enzyme activity was expected. A higher final biomass concentration could be achieved by higher initial glucose concentration or by increasing oxygen supply. Therefore the model has been validated using different initial concentration of glucose and under aerobic conditions.
Model validation
For the model validation several cultivation with different initial glucose concentration (cG0 5, 10 and 56 g dm-3) and under micro-aerobic conditions were carried out.
The comparisons of results of the experiment and simulation results, which were done by package program SCIENTIST using previous parameters, are shown in Figure 2. Since a good agreement of the result of the experiment and simulation is achieved, it can be eventuated that proposed model is valid for the cultivation, which are done under micro-aerobic conditions with the initial glucose concentration between 5 – 50 g dm-3.
Model was also validated under aerobic conditions. Experiments were carried out at oxygen concentration higher than 40% concentration of saturation using different initial glucose concentration (cG0 10 and 50 g dm-3). The results of these cultivations are shown in Figure 3. The parameter a that describes the enzyme activity unfortunately wasn’t good for the cultivations under aerobic conditions. Although in both cases the oxidative-reductive metabolism was accomplished, a lower ethanol concentration under aerobic conditions caused the lower ratio of enzyme activity and biomass concentration (Figure 4). Therefore parameter a is lower for the aerobic baker's yeast cultivations. Values of parameters a for micro-aerobic and aerobic conditions are given in Table 2.
Figure 2. Biomass wet weight (a) and volume activity (b) changes with time under micro-aerobic conditions (DO = 10 %). cG0 5 g dm-3, cG0 10 g dm-3, ▲ cG0 30 g dm-3, ▼ cG0 56 g dm-3 — model
Figure 3 Biomass wet weight (a) and volume activity (b) changes with time under micro-aerobic conditions (DO = 10 %). cG0 5 g dm-3, ▼ cG0 50 g dm-3 — model
In Figure 4, the comparison of the specific activities obtained under micro-aerobic and aerobic conditions, is shown. It can be seen that using higher oxygen feeding rate, lower ADH productivity was achieved. From that reason parameters a, which directly determines the volume activity values, is lower for the aerobic baker's yeast cultivations. Values of parameters a for micro-aerobic and aerobic conditions are shown in Table 2.
Figure 4 The specific ADH activity under the micro-aerobic (DO =10 %) and aerobic (DO = 40 %) conditions (cG0 50 g dm-3). ● micro-aerobic conditions, ○ aerobic conditions
Table 2 Parameter a for the micro-aerobic (DO = 10 %) and aerobic (DO = 40 %) condition
Parameter / Micro-aerobic conditions / Aerobic conditionsa [U g-1] / 0.400 0.0532 / 0.099 0.0121
Conclusion
Using statistical model evaluation, it is shown that the results of the proposed unstructured mathematical model for the baker's yeast growth in the batch bioreactor achieved good fitting with the results of the experiment.
Mathematical model is valid for the cultivations that are done under micro-aerobic conditions with the initial glucose concentration between 5 – 50 g dm-3.
Activity of enzyme ADH increases with baker's yeast growth. Using higher initial glucose concentration, higher volume activity of enzyme ADH was achieved.
A lower ratio of enzyme activity and biomass concentration under aerobic conditions is caused by the lower produced ethanol under these conditions. For that reason parameter a that describes ADH production is lower for the aerobic baker's yeast cultivations.
List of symbols
amodel parameter for the enzyme production, U gWW-1
ASspecific activity of the ADH enzyme, U mgWW-1
AVvolume activity of the ADH enzyme, U cm-3
bmodel parameter for the enzyme deactivation, h-1
cEt ethanol concentration, g dm-3
cG glucose concentration, g dm-3
cOoxygen concentration, g dm-3
cO,Soxygen concentration of saturation, g dm-3
cX biomass wet weight , gWW dm-3
DOrelative dissolved oxygen concentration, %, -
KEtethanol saturation constant, g dm-3
KGglucose saturation constant, g dm-3
kLatotal volumetric mass transfer coefficient [h-1]
KOoxygen saturation constant, g dm-3
rEt,max maximal ethanol oxidation rate, g gWW-1 h-1
rEt,OX specific ethanol oxidation rate, g gWW-1 h-1
rEt,pr specific ethanol production rate rate, h-1
rEt,upspecific ethanol consumption rate rate, g gWW-1 h-1
rGspecific glucose consumption rate, g gWW-1 h-1
rG,maxmaximal glucose consumption rate, g gWW-1 h-1
rG,OXspecific glucose consumption rate by oxidative path, g gWW-1 h-1