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Developing a kinetic model for co-culture of yogurt starter bacteria growth in pH controlled batch fermentation
Accepted Manuscript Developing a kinetic model for co-culture of yogurt starter bacteria growth in pH controlled batch fermentation Marzieh Aghababaie, Morteza Khanahmadi, Masoud Beheshti PII: DOI: Reference:
S0260-8774(15)00224-1 http://dx.doi.org/10.1016/j.jfoodeng.2015.05.013 JFOE 8170
To appear in:
Journal of Food Engineering
Received Date: Revised Date: Accepted Date:
7 May 2014 28 April 2015 9 May 2015
Please cite this article as: Aghababaie, M., Khanahmadi, M., Beheshti, M., Developing a kinetic model for co-culture of yogurt starter bacteria growth in pH controlled batch fermentation, Journal of Food Engineering (2015), doi: http://dx.doi.org/10.1016/j.jfoodeng.2015.05.013
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Developing a kinetic model for co-culture of yogurt starter bacteria growth in pH controlled batch fermentation Marzieh Aghababaiea, Morteza Khanahmadib, Masoud Beheshti* c a
Biotechnology Department, Faculty of Advanced Sciences and Technologies, University of Isfahan, Isfahan, IRAN, Email:[email protected]
b
Agricultural Engineering Department, Isfahan Center for Research on Agricultural Science and Natural Resources, Isfahan, IRAN, Email: [email protected] c
Chemical Engineering Department, Engineering Faculty, University of Isfahan, Isfahan, IRAN, Email: [email protected]
Abstract Streptococcus thermophilus and Lactobacillus bulgaricus are yogurt starter cultures widely used in the dairy industry. Co-culture of these bacteria leads to higher biomass yield than their separate single strain culture because of the proto-cooperation between the two species. In the present study, a kinetic model was developed for the growth and lactic acid production by these two bacteria in pH-controlled co-cultures. This model quantifies the effects of pH, temperature, lactic acid, carbon and nitrogen substrate concentrations, and the influence of each bacterium on the growth of the other. The latter effect was described by considering the calculated concentration of metabolites produced by each of the bacterium which stimulate the growth of the other. The model was validated by the experimental data obtained from a set of 12 experiments which were designed using the response surface methodology. Key words: Streptococcus thermophilus; Lactobacillus bulgaricus; kinetic modeling; single strain culture; co-culture; proto-cooperation
Nomenclature:
1
a
Non-growth associated production coefficient for lactic acid (g lactic acid /g biomass)
b
Growth associated production coefficient for lactic acid (g lactic acid /(g biomass.h))
C1
First coefficient of effect of pH on growth rate
C2
Second coefficient of effect of pH on growth rate
C3
Third coefficient of effect of pH on growth rate
Cf
Concentration of metabolites produced by S. thermophilus, which stimulate the growth of L. bulgaricus (μg .L-1)
CHLa
Concentration of undissociated lactic acid (g/L)
CLa
Concentration of lactate ion (g/L)
CP
Concentration of product (lactic acid)(g/L)
Cpep
Concentration of metabolites produced by L. bulgaricus which stimulate the growth of S. thermophilus (μg .L-1)
CSC
Concentration of carbon substrate (g/L)
CSN
Concentration of nitrogen substrate (g/L)
Ea
activation energy of effect of temperature on grow (KJ/gmole(
fji
Functions that demonstrated the effect of parameter j on the growth of bacterium i
Ga
Free energy of effect of temperature on growth (KJ/gmole(
gf
Growth associated production coefficient for metabolites which produced by S. thermophilus (μg.g-1)
gpep
Growth associated production coefficient for metabolites which produced by L. bulgaricus(μg.g-1)
hf
Non-growth associated production coefficient for metabolites which produced by S. thermophilus (μg.g-1.h-1)
hpep
Non-growth associated production coefficient for metabolites which produced by L. bulgaricus (μg.g-1.h-1)
Kc
Monod parameter for carbon source (g/l)
Kf
Monod parameter for metabolites which produced by S. thermophilus (μg.L-1)
KHla
Undissociated lactic acid inhibition parameter (g/L)
KLa
Lactate inhibition parameter (g/L)-1
KN
Monod parameter for nitrogen source (g/L)
KP
Second lactate inhibition parameter (g/L)-1
2
Kpep
Monod parameter for metabolites which produced by of L. bulgaricus (μg .L-1)
R
Universal gas constant (8.314 K J/gmole/K)
T
Temperature (K)
qf
Consumption coefficient for metabolites which produced by of S. thermophilus and consumed by L. bulgaricus (μg.g-1)
qpep
Consumption coefficient for metabolites which produced by of S. thermophilus and consumed by L. bulgaricus (μg.g-1)
W
Coefficient in the function of effect of S. thermophilus on L. bulgaricus
X
Biomass concentration (g/L)
YSNx
Theoretical bacteria yield on nitrogen substrate (g biomass/g nitrogen)
Z
Coefficient in the function of effect of L. bulgaricus on S. thermophilus
μ
Specific grow rate of bacteria (1/h)
μmax
maximum specific grow rate of bacteria in pure culture (1/h)
δn
Biomass yield on nitrogen substrate (g biomass/g nitrogen)
Superscripts(i): L
L. bulgaricus
S
S. thermophiles
m
Mixed cultures
Subscripts of functions (j): T
Effect of temperature
pH
Effect of pH
C
Effect of carbon substrate
N
Effect of nitrogen substrate
La
Effect of lactate concentration
Hla
Effect of Lactic acid concentration
3
1.
Introduction
Streptococcus thermophilus (S.thermophilus) and Lactobacillus delbrueckii ssp bulgaricus (L. bulgaricus) are homofermentative lactic acid bacteria which are the traditional starter cultures in yogurt and cheese production. Generally, they are grown in separate pure culture batches and then mixed together in appropriate proportions to produce starter cultures (Beal et al. 1989, Beal and Corrieu 1998). Mostly, the ratio of 1:1 (chain: chain) of S. thermophilus to L. bulgaricus is desired in starter culture, which figures of 5-10 S. thermophilus: 1 L. bulgaricus may well become the accepted norm (Tamime and Robinson, 2007). However, their propagation in the same batch seems to be beneficial and saves both time and energy. The main challenge in the mixed culture is to set and control growth conditions such that the desired final population ratio of the two bacteria can be achieved. The major controllable parameters in this regards are temperature, pH, and inoculation ratio (Beal and Corrieo 1991, Beal et al. 1994, Beal and Corrieu 1998). Interaction of the species should be included for the mixed culture in the model. S. thermophilus and L. bulgaricus have an interaction in the yogurt which is termed proto-cooperation and is a symbiotic relationship between these two species and a mutual metabolism with positive effects on the fermented product (Pette and Lolkema 1950, Angelov et al. 2009). Maximum population (Amoroso et al. 1989, Beal et al. 1994), specific growth rate (Moon and Reinhold 1976, MacBean et al. 1979, Driessen et al. 1982), maximum lactic acid concentration (O'Leary and Woychik 1976, Beal et al. 1994, Beal and Corrieu 1998), and lactic acid production rate (Rajagopal and Sandine 1990) were all increased in mixed culture as compared with those of separate single strain cultures. In this symbiotic relationship each of the bacteria produces substances favorable for the other (Tamime and Robinson 4
2007, Angelov et al. 2009). It has been discovered that, S. thermophilus supports the growth of L. bulgaricus mainly by producing lactic and formic acid and creating the necessary anaerobic conditions for L. bulgaricus growth by the utilization of the dissolved oxygen in milk and formation of CO2 (Suzuki et al. 1986(a), 1986(b), Beal et al. 1994, Tamime and Robinson 2007, Angelov et al. 2009). On the other hand, L. bulgaricus possesses more proteolytic enzymes than S. thermophilus (Rajagopal and Sandine 1990, Tamime and Robinson 2007). In this way, L. bulgaricus stimulates the growth of S. thermophilus by releasing amino acids like glycine and histidine, and short peptides into the growth medium (Tamime and Robinson 2007, Angelov et al. 2009). Although the effect of the association of these bacteria is often positive, it can also be neutral or detrimental depending on the bacterial strains employed, the type of milk, the method used to heat the milk, and the temperature of milk (Tamime and Robinson 2007, Angelov et al. 2009). Whey is the byproduct of cheese manufacturing plants and a cheap nutritious material. It contains all of the lactose, non-protein nitrogen, organic acids, ash, and water-soluble vitamins of the milk (Tamime and Robinson 2007). Whey has been used as a carbon source to produce lactic acid bacteria and lactic acid (Beal et al. 1989, Bassi et al. 1991, Parente and Zottola 1991, Chiarini et al. 1992, Jokar and Karbassi 2009, Aghababaie et al. 2014). The proto-cooperation between S. thermophilus and L. bulgaricus may be different in whey medium which is enriched only by yeast extract. Mathematical models are powerful tools in simulation and control of such dynamic processes. Various aspects of the metabolism and growth of these bacteria in single strain culture have been reported in previous studies (Beal et al. 1989, Beal and Corrieu 1998). Several models have been proposed to formulate the effect of 5
factors, like temperature, pH, concentration of carbon, nitrogen sources, and the main inhibitory metabolite (i.e. lactic acid), in the kinetic modeling of L. helveticus (Schepers et al., 2002b), L. deibrueckii (Luedeking and Piret, 2000), L. casei (Alvarez et al., 2010), and L. bulgaricus (Venkatesh et al. 1993, Gadgil and Venkatesh 1996, Luedeking and Piret 2000, Schepers et al. 2002b, Alvarez et al. 2010). Despite the abundance of mixed cultures in nature, there are limited number of researches on kinetics of these systems mainly due to the complexity of their dynamics and difficulty of their analysis and control (Katoh et al. 1999). In one study, a model was developed for this system with the assumption that no interaction exists between the two bacteria (Sodini et al. 2000). In another attempt, the Volterra equation for competitive growth was used to model the mixed culture of the two bacteria in a batch fermentation without pH control (Berkman et al. 1990). The model has successfully covered experimental data; however, it contains no term to describe the dependency of growth rate on various factors such as temperature, pH, and medium composition. In the present study, a kinetic model was developed for the growth kinetics of L. bulgaricus and S. thermophilus in co-culture. To overcome the shortages of the abovementioned models, both environmental effects, i.e. temperature and pH , and interaction of the microorganisms are considered in this model. The co-culture model was an extension of the single strain kinetic model of S. thermophilus and L. bulgaricus which was validated in a previous study (Aghababaie et al. 2014). In this co-culture model, the effect of each bacterium on the other was considered in different terms. Response surface methodology (RSM) was implemented to investigate the effect of pH and temperature on the growth, lactic acid production, total population, and final percentage of S. thermophilus in the co-culture of S. 6
thermophilus and L. bulgaricus. The coefficients of the co-culture model were determined and the model was validated for the co-culture experiments. 2.
Theory
In a previous study by the authors, the simple Malthusian growth kinetic model was applied in combination with the terms that describe the influence of various factors (Aghababaie et al. 2014). The effect of carbon and nitrogen substrates, temperature, pH, and dissociated and undissociated forms of lactic acid were considered in the single strain kinetic model. These expressions are depicted in Table 1. Parameters of these expressions were estimated previously in the study of single strain kinetic modeling of these strains (Aghababaie et al. 2014). This kinetic model for the growth of bacterium i was described as follows:
dXi dt
i i i i i imax fTi f pH fScfSn f Laf HLaXi
(1)
In order to describe the co-culture kinetic model, fji was inserted into the single strain kinetic model to describe the effect of one bacterium on the other. dXim i i i i i imax fTi f pH fScfSn f Laf HLaf ji Xim dt
(2)
In Eq (2), fij is the effect of bacterium j on specific growth rate of bacterium i. To comply with the proto-cooperation effect, it is assumed that bacterium j produces metabolites which eventually stimulate the growth of the other bacterium. In single strain culture model, this term was equal to 1.0. Table 1. 2.1. Effect of L. bulgaricus on S. thermophilus (fSL) Short peptides and amino acids which have been released due to the proteolytic activity of L. bulgaricus in whey proteins, would stimulate the growth of S.
7
thermophilus (Tamime and Robinson 2007, Angelov et al. 2009). Accumulation rate of these metabolites was determined as below:
dC pep dX mL dX mS L g pep hpep X m q pep dt dt dt
(3)
The effect of these metabolites on the growth rate of S. thrmophilus could be described in the Monod type model as follows: f LS Z
C pep
(4)
C pep K pep
2.2. Effect of S .thermophilus on L. bulgaricus ( f SL ) S. thermophilus produces lactic and formic acids and carbon dioxide which reduces the pH of the medium and makes it suitable for the growth of L. bulgaricus in milk (Tamime and Robinson 2007, Angelov et al. 2009). While pH was constant during the fermentation, this effect is negligible in this study. However, the effect of dissociated and undissociated lactic acid concentrations was considered in the model. Furthermore, formic acid and carbon dioxide stimulate the growth of L. bulgaricus through other mechanisms. The accumulation rate of formic acid could be estimated by the following equation:
dCf dXSm dX Lm S gf hf Xm qf dt dt dt
(5)
Formic acid is consumed by L. bulgaricus while some portion of CO2 transfers to gas phase and some changes to other forms of CO2 (HCO-3, HCO-2), based on the pH of the fermentation. In this issue, the effect of carbon dioxide was negligible. Thus, the effect of S. thermophilus on L. bulgaricus ( f SL ) could be described by the concentration of formic acid in Monod type model as below:
f SL W
Cf Cf K f
(6) 8
2.3. Lactic acid production rate The Luedeking-Piret equation was applied for describing lactic acid production rate (rp) in co-culture as follows (Luedeking and Piret 2000): rp
dP dXSm dX Lm aS bSXSm a L b L X Lm dt dt dt
(7)
2.4. Substrates consumption rates Carbon substrate is converted to lactic acid, biomass of both S. thermophilus and L. bulgaricus, and trace amounts of secondary metabolites. The rate of carbon substrate consumption is equal to the sum of the product and biomass formation rates (Venkatesh et al. 1993) and is obtained by the following equation:
dSc dX mS dX mL dP 1.19 1.19 0.95 i dt dt dt dt
(8)
The usable nitrogen content in yeast extract is converted into biomass (Aghababaie et al. 2014). The rate of nitrogen substrate consumption is given below:
dSn dXSm dX Lm SnM LnM dt dt dt
(9)
2.5. Model simulation The simulating mathematical model for single strain culture is constructed by combining the abovementioned set of governing differential equations:
9
1 0 1.19 S a S nM q pep g f
3.
0 1 1.19 aL L nM
g pep qf
0 0 0 0 1 0.95 0 1 0 0 0 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 1 0
dX mS dt dX mL S S S S S S S S S f f f f f f f X 0 dt max T pH La HLa S N SC L m 0 dSc L f L f L f L f L f L f L f LX L 0 dt max T pH La HLa S N SC S m 0 dPi 0 S S b X m b L X mL dt 0 dS n 0 0 dt hpep X mL 1 dC pep h f X mS dt dC f dt
(10)
Materials and methods
3.1. Microorganism and culture media Single strain batch cultures of Streptococcus thermophilus and Lactobacillus bulgaricus in whey and yeast extract medium with different pH and temperatures have been previously described (Aghababaie et al. 2014). Streptococcus thermophilus PTCC 1738 (ATCC 19258) was obtained from microbial collection of the Iranian Research Organization for Science and Technology. Lactobacillus delbrockii ssp bulgaricus was isolated from a traditional yogurt. Cultures were prepared from frozen stocks at 1% (v/v), and incubated for 18h at 40 °C. In coculture experiments, initial population ratio of S. thermophilus to total population (Xs/XT) in all of the experiments was considered as 50%. Medium composition in co-culture experiments were similar to that in single strain culture’s which was described in details previously (Aghababaie et al. 2014). The medium contained a sterile solution of 100 g/L whey and 10 g/L yeast extract in a 1.0 liter in-house manufactured bioreactor.
10
3.2. Design of experiments Central Composite, Uniform Precision Design of RSM was applied with 12 runs in order to estimate the effects of pH and temperature on the growth and lactic acid production of S. thermophilus and L. bulgaricus in co-culture. This design included 4 factorials, 4 axials, and 4 center points that were considered with different pH and temperature levels for co-culture experiments (Table 2). Analysis of variance was performed for maximum cell population (X max) and maximum specific growth rate (µmax) of each bacterium, total population of co-culture (XT), ratio of maximum S. thermophilus concentration to total population (X s/XT), and total produced lactic acid. Optimum pH and temperature for the growth of these bacteria were estimated by RSM analysis. Analysis was performed using SAS software (version 9.0; SAS Institute Inc., Cary, NC, USA). Table 2. 3.3. Analysis Lactic acid production rate in the fermenter was determined by the intermittent addition of 5N NaOH at appropriate time intervals using a peristaltic pump (Beal and Corrieu 1995). The fermenter was sampled at 30-minute intervals and placed in
the refrigerator (Beal et al. 1989). M17 and MRS agar mediums were used for enumeration of S. thermophilus and L. bulgaricus, respectively, which were used for CFU counting of co-culture during fermentation (Berkman et al. 1990). The microbial growth was measured by microscopy using a Thoma counting chamber with 0.02 mm depth according to their different morphology (Aghababaie et al. 2014). The biomass average specific dry weight (g/cell) was determined by measuring the weight of a dried sample containing a predetermined number of the bacterial cells cultivated in single strain cultures. Initial concentration of lactose in 11
whey solution, as determined by colorimetric dinitrosalicylic acid (DNS) method, was about 60 g/l. Lactose concentration during fermentation has a linear correlation with the produced lactic acid concentration (Beal and Corrieu 1995). To estimate the molar concentration of lactose during the fermentation the following equation (Beal and Corrieu 1995) was used:
CSC [CSC0 / 342 (m / 90).(CP )] 342
(11)
In this equation, m was about -0.54 and -0.61 for S. thermophilus and L. bulgaricus, respectively, in single strain cultures and -0.57 for their co-culture. Here, Csc0 was the initial concentration of lactose (Beal and Corrieu 1995). The yield of biomass on nitrogen substrate (YSNx) for some lactic acid bacteria is about 1.0 (g biomass/g nitrogen) (Nielsen et al. 1991, Schepers et al. 2002b).The nitrogen substrate concentration throughout the co-culture fermentation can be calculated through the linear equation:
CSN CSN0 (1 / YSNx )( X i )
(12)
where, CSN was the initial concentration of yeast extract. 3.4. Parameter estimation and model solution The single strains parameters have been estimated previously using SBToolbox2 on Matlab 7.12.0. (R2011a,The MathWorks Inc., Natick, MA, USA) (Aghababaie et al. 2014). The same values were used for co-culture simulation, and therefore, only the parameters of f SL and f LS , i.e. parameters of equations 3 to 6, were estimated in the present study. Particle swarm algorithm was applied in SBToolbox2 with its default options to estimate the co-culture model parameters (Vaz and Vicente 2007, 2009, Henkel et al. 2011). Experimental results related to biomass of S. thermophilus and L. bulgaricus, lactic acid, nitrogen, and carbon substrate concentrations of each experiment were the input data for SBToolbox2. 12
The particle swarm algorithm minimizes the sum of quadratic differences between measurements and simulations, and reports the minimum function which shows the appropriateness of fitting (Henkel et al. 2011). The closer the minimum function is to zero the better the fitting. Eq. (10) was solved using ode23 function of Matlab based on the Trapezoidal rule to compare the experimental data and predicted model. 4.
Results and discussion
4.1. Statistical analysis of experimental results According to the RSM analyses of S. thermophilus and L. bulgaricus single strain cultures, pH and temperature had a significant effect on the growth of these bacteria at the examined range. Optimum pH and temperature were 7 and 42.8 °C for single strain growth of S. thermophilus, and 5.2 and 44 °C for single strain growth of L. bulgaricus, respectively. RSM analysis of co-culture experiments showed that maximum population (Xmax) of each bacterium and total produced lactic acid in the bioreactor depended on the pH and temperature of the fermentation. Total population (XT) and ratio of maximum S. thermophilus population to total population (Xs/XT) were pH and temperature dependent. Thus, the desired ratio can be obtained by controlling the pH and temperature of the fermentation. Optimum pH and temperature, in order to attain maximum total population (XT) alongside the desired ratio of 83% (Xs/XT), were 6 and 46 °C, respectively. However, optimum pH and temperature for obtaining maximum population of each bacterium were different. In the co-culture experiments, optimum pH values were in the range of 6.10-6.40 for the growth of S. thermophilus, and in the range of 5.70-6.10 for the growth of 13
L. bulgaricus. Optimum temperatures were about 42 °C for both bacteria in the coculture experiments. The optimum growth conditions of each bacterium in coculture are different from that of single strain culture (Aghababaie et al. 2014). In the co-culture model, pH and temperature will affect the growth of each bacterium ,and eventually, influence the metabolite productions and microbial growth. 4.2. Co-culture vs. pure culture According to the RSM results, optimum pH and temperature to attain the maximum total populations of these bacteria in co-culture were 6.1 and 42 °C, respectively. In the optimum conditions, the maximum populations of S. themophilus and L. bulgaricus in co-culture were 8.3 and 39.5 times more than that of their single strain cultures. Thus, the presence of S. thermophilus is more beneficial for L. bulgaricus than vice versa. Total lactic acid produced in co-culture was 1.4 times that of single strain cultures. Total population in co-culture was 10 times the of sum of populations of single strain cultures. Furthermore, it should be mentioned that by producing the starters in co-culture, half of the medium would be used compared with two batches of single strain cultures. Therefore, medium, energy, and time will be saved. 4.3. Effect of L. bulgaricus on S. thermophilus in co-culture According to the results of single strain and co-culture experiments of S.thermophilus, it was observed that the growth of S. thermophilus in co-culture experiments was not much higher than that of S. thermophilus in single strain cultures (Aghababaie et al. 2014). Thus, it is revealed that the effect of L. bulgaricus on S. thermophilus depends on the medium composition. Since the whey permeate lacks milk proteins, the proteolitic activity of L.bulgaricus was not useful in the whey based mediums. 14
4.4. Effect of S. thermophilus on L. bulgaricus in co-culture The presence of S. thermophilus enhanced the growth of L. bulgaricus evident in comparison with that of single strain (Aghababaie et al. 2014). It is known that S. thermophilus grows faster than L. bulgaricus and supports the growth of L. bulgaricus mainly by producing lactic and formic acid. Moreover, S. thermophilus assimilates oxygen faster, and thus, creates favorable conditions for L. bulgaricus growth (Angelov et al., 2009). 4.5. Estimated values of parameters Estimated values for the co-culture parameters is presented in Table 2, along with that of single strain culture parameters which were determined in single strain modeling (Aghababaie et al. 2014). Minimum function reported for this set of estimated parameters was about 0.06. The minimum function is a measure of fitting error, and so, this small quantity represents high goodness of fit resulted from the values depicted in Table 3. By setting fjis as equal to 1.0, the single strain culture model is obtained. In the case of co-culture growth, this term will increase with time which demonstrates the effect of produced metabolites on the other bacterium during the fermentation. Table 3. 4.6. co-culture kinetic model validation Validity of the kinetic model for single strain culture, i.e. Eq.(1), has been tested against experimental data and good agreements have been observed between the experimental data and model predictions for the growth and lactic acid production of L. bulgaricus and S. thermophilus in single strain cultures (Aghababaie et al. 2014).
15
Practiced experiments of co-cultures were simulated by solving Eq. (10) with the parameter values shown in the Table 3. Figs. 1 and 2 depicts the experimental and model prediction of S. thermophilus and L. bulgaricus growth and lactic acid production trends. The concentration of the metabolites can also be calculated by the model simulation. In all the considered cases, there was a good agreement between the experimental data and simulated trends. This confirms the validity of the model, and especially, the way the cooperation of the two bacteria was formulated. Fig. 1 Fig. 2 While few researches have been performed on culture modeling, this model would be useful for other symbiotic relationships. The previous mixed culture model which was presented for S. thermophilus and L. bulgaricus by Berkman et al. (1990), was less mechanistic than the current model, since the effect of each bacterium on the other was considered as a function of the bacterium biomass instead of its influencing metabolite. The ratio between S. thermophilus and L. delbrueckii subsp. bulgaricus in the yogurt starter culture influences the organoleptic properties of the fermented product. A ratio of 1:1 (chain: chain) of S. thermophilus to L. bulgaricus is used for the production of conventional yogurt in many parts of the world. As mentioned before, this ratio corresponds to 5:1 ratios of single cell numbers of these two bacteria. In Some countries, the statutory regulations may stipulate the use of this ratio (Tamim and Robinson, 2007). However, a ratio of 40:60 can be used for the production of sharp flavored yoghurt, while for milder flavored yoghurt a ratio of 60:40 can be used (Tamim and Roninson, 2007). Therefore, adjustment of the 16
customer desired ratio is important and the developed model can help to predict and control the mixed culture process to attain any predetermined ratio of the two bacteria in the produced starter. 5.
Conclusion
In the present study, co-culture of yogurt starter species in whey based medium was investigated. The results showed that pH and temperature have significant effect on the growth, lactic acid production, and final population and percentage of S. thermophilus. Optimum pH and temperature to obtain the maximum population and desired ratio of 5:1 of S. thermophilus to L. bulgaricus were about 6.4 and 46 °C, respectively. In the whey based medium the effect of S. thermophilus on the growth of L.bulgaricus was more considerable than vice versa. This reveals that the proto-cooperation between S. thermophilus and L. bulgaricus depends on the medium composition and it is different in whey in comparison with milk. A kinetic model was developed to predict the behavior of co-culture growth of S. thermophilus and L. bulgaricus as a function of pH, temperature, carbon substrate, nitrogen substrate, lactic acid concentration, and their interactions. This model was capable of predicting bacterial growth at different pH and temperatures in the examined ranges in single strain and co-culture, and is useful for simulating and controlling the fermentation process of these bacteria. It could be extended for simulating growth of the bacteria in milk and in varying pH conditions. The developed model can pave the way for future studies in different mixed culture modeling efforts. 6.
Acknowledgments
This study was financially supported by the Isfahan Center for Research on Agricultural Science and Natural Resources, and the University of Isfahan. 17
7.
References
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bulgaricus in yoghurt is stimulated by carbon dioxide produced by Streptococcus thermophilus." Neth Milk Dairy J 36(135-144). Gadgil, C.J. & Venkatesh, K.V. (1996). "Structured Model for Batch Culture Growth of Lactobacillus bulgaricus." Journal of Chemical Technology and Biotechnology, 68(1): 8993. Henkel, S., Nägele, T., Hörmiller, I., Sauter, T., Sawodny, O., Ederer, M. & Heyer, A.G. (2011). "A systems biology approach to analyse leaf carbohydrate metabolism in Arabidopsis thaliana " EURASIP Journal on Bioinformatics and Systems Biology, 2: 1-10. Jokar, A. & Karbassi, A. (2009). "Determination of Proper Conditions for the Production of Crude Beta-galactosidase Using Lactobacillus delbrueckii ssp. bulgaricus." Journal of Agricaltural Science and Technology, 11: 301-308. Katoh, T., Yuguchi, D., Yoshii, H., Shi, H. & Shimizu, K. (1999). "Dynamics and modeling on fermentative production of poly (β-hydroxybutyric acid) from sugars via
19
lactate by a mixed culture of Lactobacillus delbrueckii and Alcaligenes eutrophus." J Biotechnol 67(2-3): 113-134. Luedeking, R. & Piret, E.L. (2000). "A kinetic study of the lactic acid fermentation. Batch process at controlled pH." Biotechnology and Bioengneering, 67(6): 636 - 644. MacBean, R.D., Hall, R.J. & Linklater, P.M. (1979). "Analysis of pH-stat continuous cultivation and the stability of the mixed fermentation in continuous yoghurt production." Biotechnology and Bioengneering, 21: 1517-1541. Moon, N.J. & Reinhold, G.W. (1976). "Commensalism and competition in mixed cultures of Lactobacillus bulgaricus and Streptococcus thermophilus." Journal of milk and food Technology, 39: 337-341. Nielsen, J., Nikolajsen, K. & Villadsen, J. (1991). "Structured modeling of microbial system:IIExperimental verification of structured lactic acid fermentaion model." Biotechnology and Bioengneering, 38: 11-23. O'Leary, V.S. & Woychik, J.H. (1976). "Utilization of lactose, glucose and galactose by a mixed culture of Streptococcus thermophiIus and Lactobacillus bulgaricus in milk treated with lactase enzyme." Applied Environmental Microbiology, 32: 89-94. Parente, E. & Zottola, E.A. (1991). "Growth of Thermophilic Starters in Whey Permeate Media." Jouranl of Dairy Science, 74: 20-28. Pette, J.W. & Lolkema, H. (1950). "Yoghurt. I. Symbiosis and antibiosis in mixed culture of Lactobacillus bulgaricus and Streptococcus therrnophilus." Netherland Milk and Dairy Journal, 4: 197-208. Rajagopal, S.N. & Sandine, W.E. (1990). "Associative growth and proteolysis of Streptococcus thermophilus and Lactobacillus bulgaricus in skim milk." Journal of Dairy Science, 69: 2558-2568. Schepers, A.W., Thibault, J. & Lacroix, C. (2002b). "Lactobacillus helveticus growth and lactic acid production during pH-controlled batch cultures in whey permeate/yeast extract medium. Part II: kinetic modeling and model validation." Enzyme Microbiology and Technology, 30(2): 187-194. 20
Sodini, I., Latrille, E. & Corrieo, G. (2000). "Identification of interacting mixed cultures of lactic acid bacteria by their exclusion from a model predicting the acidifying activity of non-interacting mixed cultures." Applied Microbiology and Biotechnology, 54: 715-718. Suzuki, I., Kato, S., Kitada, T., Yano, N. & Morichi, T. (1986(a)). "Growth of Lactobaci//us bulgaricus in Milk. 1.Cell Elongation and the Role of Formic Acid in Boiled Milk." Journal of Dairy Science, 28: 311-320. Suzuki, I., Kato, S., Kitada, T., Yano, N. & Morichi, T. (1986(b)). "Growth o f Lactobacillus bulgaricus in Milk. 2. Characteristics of Purine Nucleotides, Pyrimidine Nucleotides, and Nucleic Acid Synthesis." Journal of Dairy Science, 69: 971-980. Tamime, A.E. & Robinson, R.K. (2007). Tamime and Robinson's Yoghurt Science and technology. New York, CRC press. Vaz, A.I.F. & Vicente, L.N. (2007). " A particle swarm pattern search method for bound constrained global optimization." Journal of Global Optimization, 39: 197-219. Vaz, A.I.F. & Vicente, L.N. (2009). "PSwarm: a hybrid solver for linearly constrained global derivative-free optimization." Optimization Methods and Software, 24(4-5). Venkatesh, K.V., Okos, M.R. & Wankat, P.C. (1993). "Kinetic Model of Growth and Lactic Acid Production from Lactose by Lactobacillus bulgaricus." Process Biochemestry, 28: 231-241.
21
Tables
Table 1. Functions of the kinetic model described previously for single strain cultures
Equation
Function
e
fT
Function of temperature (fT)
E a RT (
1 Ae
f pH
Function of pH (fpH)
G a ) RT
C1 (pHopt pH) 2 C 2 (pHopt pH) 2 C3
Function of carbon substrate (fSc)
fSC
Csc Csc K c
Function of nitrogen substrate (fSN)
fSN
CSN CSN K N
Function of lactate (fLa)
f La ek i .CLa
Function of lactic acid (fHla)
1 f Hla K p (C Hla K Hla ) 1 e
22
Figure
Figures
(a)
(b)
(c)
(d) Fig 1. Experimental data (symbols) and model prediction (lines) - biomass and lactic acid vs. time for co-culture of S. thermopnilus and L. bulgaricus (a) 38.0°C and pH=5.70 (b) 38.0°C and pH =6.50 (c) 46.0 °C and pH=5.70 (d) 46.0 °C and pH=6.50
(a)
(b)
(c)
(d) Fig 2. Experimental data (symbols) and model prediction (lines) - biomass and lactic acid vs. time for co-culture of S. thermopnilus and L. bulgaricus; (a) 36.3 °C and pH=6.10; (b) 42.0 °C and pH=5.53 ;(c) 42.0 °C and pH= 6.66 ;(d) 42.0 °C and pH=6.10
Table 2. Experimental conditions based on RSM for batch cultures
RUN 1 2 3 4 5 6 7 8 9 10 11 12
Coded values L. bulgaricus Tc pHT(°C) PH c -1 -1 40.0 4.90 -1 1 40.0 6.50 1 -1 48.0 4.90 1 1 48.0 6.50 -1.41 0 38.3 5.70 1.41 0 49.6 5.70 0 -1.4144.0 4.56 0 1.4144.0 6.83 0 0 44.0 5.70 0 0 44.0 5.70 0 0 44.0 5.70 0 0 44.0 5.70
23
S. thermophilus Co-culture T (°C) pH T (°C) pH 36.0 5.7038.0 5.70 36.0 7.3038.0 6.50 44.0 5.7046.0 5.70 44.0 7.3046.0 6.50 34.3 6.5036.3 6.10 45.6 6.5047.6 6.10 40.0 5.3642.0 5.53 40.0 7.6342.0 6.66 40.0 6.5042.0 6.10 40.0 6.5042.0 6.10 40.0 6.5042.0 6.10 40.0 6.5042.0 6.10
Table 3. Parameters of the proposed model Parameter μ max,L AL E aL GaL pHoptL C1L C2L C3L KcL K NL KpL KLaL kHLaL aL bL δn,L μ max,S AS E aS GaS pHoptS C1S C2S C3S KcS K NS KpS KLaS kHLaS aS bS δns gf hf qf gp hp qp Kf Kpep Z W
value source 1.95 SSC of L. bulgaricus (Aghababaie et al. 2014) 1.9E+6 SSC of L. bulgaricus (Aghababaie et al. 2014) 80 SSC of L. bulgaricus (Aghababaie et al. 2014) 55430 SSC of L. bulgaricus(Aghababaie et al. 2014) 5.249 SSC of L. bulgaricus(Aghababaie et al. 2014) 6.64 SSC of L. bulgaricus (Aghababaie et al. 2014) 69.32 SSC of L. bulgaricus(Aghababaie et al. 2014) 2.77 SSC of L. bulgaricus (Aghababaie et al. 2014) 2.48 SSC of L. bulgaricus (Aghababaie et al. 2014) 124.7 SSC of L. bulgaricus (Aghababaie et al. 2014) 0.4979 SSC of L. bulgaricus (Aghababaie et al. 2014) 0.44 SSC of L. bulgaricus (Aghababaie et al. 2014) 0.00001 SSC of L. bulgaricus (Aghababaie et al. 2014) 0.7 SSC of L. bulgaricus (Aghababaie et al. 2014) 0.6 SSC of L. bulgaricus (Aghababaie et al. 2014) 1.08 SSC of L. bulgaricus (Aghababaie et al. 2014) 1.177 SSC of S. thermophilus (Aghababaie et al. 2014) 1.2E+6 SSC of S. thermophilus (Aghababaie et al. 2014) 130 SSC of S. thermophilus (Aghababaie et al. 2014) 52160 SSC of S. thermophilus (Aghababaie et al. 2014) 6.87 SSC of S. thermophilus (Aghababaie et al. 2014) 45.42 SSC of S. thermophilus (Aghababaie et al. 2014) 11.25 SSC of S. thermophilus (Aghababaie et al. 2014) 0.123 SSC of S. thermophilus (Aghababaie et al. 2014) 0.000001 SSC of S. thermophilus (Aghababaie et al. 2014) 253.1 SSC of S. thermophilus (Aghababaie et al. 2014) 52.86 SSC of S. thermophilus (Aghababaie et al. 2014) 0.3259 SSC of S. thermophilus (Aghababaie et al. 2014) 0.0444 SSC of S. thermophilus (Aghababaie et al. 2014) 1.54 SSC of S. thermophilus (Aghababaie et al. 2014) 0.52 SSC of S. thermophilus (Aghababaie et al. 2014) 0.98 SSC of S. thermophilus (Aghababaie et al. 2014) 1.54 Co-culture (this study) 2 Co-culture (this study) 2 Co-culture (this study) 0.21 Co-culture (this study) 1.1 Co-culture (this study) 2 Co-culture (this study) 2 Co-culture (this study) 5 Co-culture (this study) 180 Co-culture (this study) 50 Co-culture (this study)
SSC: Single Strain Culture
24
Highlights A co-culture growth kinetic model was developed by the extension of single strain models. Influence of each bacterium on the other was considered in the co-culture model. The model parameters were estimated with the use of particle swarm algorithm. The model was able to simulate experimental data properly.
25
S0260-8774(15)00224-1 http://dx.doi.org/10.1016/j.jfoodeng.2015.05.013 JFOE 8170
To appear in:
Journal of Food Engineering
Received Date: Revised Date: Accepted Date:
7 May 2014 28 April 2015 9 May 2015
Please cite this article as: Aghababaie, M., Khanahmadi, M., Beheshti, M., Developing a kinetic model for co-culture of yogurt starter bacteria growth in pH controlled batch fermentation, Journal of Food Engineering (2015), doi: http://dx.doi.org/10.1016/j.jfoodeng.2015.05.013
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Developing a kinetic model for co-culture of yogurt starter bacteria growth in pH controlled batch fermentation Marzieh Aghababaiea, Morteza Khanahmadib, Masoud Beheshti* c a
Biotechnology Department, Faculty of Advanced Sciences and Technologies, University of Isfahan, Isfahan, IRAN, Email:[email protected]
b
Agricultural Engineering Department, Isfahan Center for Research on Agricultural Science and Natural Resources, Isfahan, IRAN, Email: [email protected] c
Chemical Engineering Department, Engineering Faculty, University of Isfahan, Isfahan, IRAN, Email: [email protected]
Abstract Streptococcus thermophilus and Lactobacillus bulgaricus are yogurt starter cultures widely used in the dairy industry. Co-culture of these bacteria leads to higher biomass yield than their separate single strain culture because of the proto-cooperation between the two species. In the present study, a kinetic model was developed for the growth and lactic acid production by these two bacteria in pH-controlled co-cultures. This model quantifies the effects of pH, temperature, lactic acid, carbon and nitrogen substrate concentrations, and the influence of each bacterium on the growth of the other. The latter effect was described by considering the calculated concentration of metabolites produced by each of the bacterium which stimulate the growth of the other. The model was validated by the experimental data obtained from a set of 12 experiments which were designed using the response surface methodology. Key words: Streptococcus thermophilus; Lactobacillus bulgaricus; kinetic modeling; single strain culture; co-culture; proto-cooperation
Nomenclature:
1
a
Non-growth associated production coefficient for lactic acid (g lactic acid /g biomass)
b
Growth associated production coefficient for lactic acid (g lactic acid /(g biomass.h))
C1
First coefficient of effect of pH on growth rate
C2
Second coefficient of effect of pH on growth rate
C3
Third coefficient of effect of pH on growth rate
Cf
Concentration of metabolites produced by S. thermophilus, which stimulate the growth of L. bulgaricus (μg .L-1)
CHLa
Concentration of undissociated lactic acid (g/L)
CLa
Concentration of lactate ion (g/L)
CP
Concentration of product (lactic acid)(g/L)
Cpep
Concentration of metabolites produced by L. bulgaricus which stimulate the growth of S. thermophilus (μg .L-1)
CSC
Concentration of carbon substrate (g/L)
CSN
Concentration of nitrogen substrate (g/L)
Ea
activation energy of effect of temperature on grow (KJ/gmole(
fji
Functions that demonstrated the effect of parameter j on the growth of bacterium i
Ga
Free energy of effect of temperature on growth (KJ/gmole(
gf
Growth associated production coefficient for metabolites which produced by S. thermophilus (μg.g-1)
gpep
Growth associated production coefficient for metabolites which produced by L. bulgaricus(μg.g-1)
hf
Non-growth associated production coefficient for metabolites which produced by S. thermophilus (μg.g-1.h-1)
hpep
Non-growth associated production coefficient for metabolites which produced by L. bulgaricus (μg.g-1.h-1)
Kc
Monod parameter for carbon source (g/l)
Kf
Monod parameter for metabolites which produced by S. thermophilus (μg.L-1)
KHla
Undissociated lactic acid inhibition parameter (g/L)
KLa
Lactate inhibition parameter (g/L)-1
KN
Monod parameter for nitrogen source (g/L)
KP
Second lactate inhibition parameter (g/L)-1
2
Kpep
Monod parameter for metabolites which produced by of L. bulgaricus (μg .L-1)
R
Universal gas constant (8.314 K J/gmole/K)
T
Temperature (K)
qf
Consumption coefficient for metabolites which produced by of S. thermophilus and consumed by L. bulgaricus (μg.g-1)
qpep
Consumption coefficient for metabolites which produced by of S. thermophilus and consumed by L. bulgaricus (μg.g-1)
W
Coefficient in the function of effect of S. thermophilus on L. bulgaricus
X
Biomass concentration (g/L)
YSNx
Theoretical bacteria yield on nitrogen substrate (g biomass/g nitrogen)
Z
Coefficient in the function of effect of L. bulgaricus on S. thermophilus
μ
Specific grow rate of bacteria (1/h)
μmax
maximum specific grow rate of bacteria in pure culture (1/h)
δn
Biomass yield on nitrogen substrate (g biomass/g nitrogen)
Superscripts(i): L
L. bulgaricus
S
S. thermophiles
m
Mixed cultures
Subscripts of functions (j): T
Effect of temperature
pH
Effect of pH
C
Effect of carbon substrate
N
Effect of nitrogen substrate
La
Effect of lactate concentration
Hla
Effect of Lactic acid concentration
3
1.
Introduction
Streptococcus thermophilus (S.thermophilus) and Lactobacillus delbrueckii ssp bulgaricus (L. bulgaricus) are homofermentative lactic acid bacteria which are the traditional starter cultures in yogurt and cheese production. Generally, they are grown in separate pure culture batches and then mixed together in appropriate proportions to produce starter cultures (Beal et al. 1989, Beal and Corrieu 1998). Mostly, the ratio of 1:1 (chain: chain) of S. thermophilus to L. bulgaricus is desired in starter culture, which figures of 5-10 S. thermophilus: 1 L. bulgaricus may well become the accepted norm (Tamime and Robinson, 2007). However, their propagation in the same batch seems to be beneficial and saves both time and energy. The main challenge in the mixed culture is to set and control growth conditions such that the desired final population ratio of the two bacteria can be achieved. The major controllable parameters in this regards are temperature, pH, and inoculation ratio (Beal and Corrieo 1991, Beal et al. 1994, Beal and Corrieu 1998). Interaction of the species should be included for the mixed culture in the model. S. thermophilus and L. bulgaricus have an interaction in the yogurt which is termed proto-cooperation and is a symbiotic relationship between these two species and a mutual metabolism with positive effects on the fermented product (Pette and Lolkema 1950, Angelov et al. 2009). Maximum population (Amoroso et al. 1989, Beal et al. 1994), specific growth rate (Moon and Reinhold 1976, MacBean et al. 1979, Driessen et al. 1982), maximum lactic acid concentration (O'Leary and Woychik 1976, Beal et al. 1994, Beal and Corrieu 1998), and lactic acid production rate (Rajagopal and Sandine 1990) were all increased in mixed culture as compared with those of separate single strain cultures. In this symbiotic relationship each of the bacteria produces substances favorable for the other (Tamime and Robinson 4
2007, Angelov et al. 2009). It has been discovered that, S. thermophilus supports the growth of L. bulgaricus mainly by producing lactic and formic acid and creating the necessary anaerobic conditions for L. bulgaricus growth by the utilization of the dissolved oxygen in milk and formation of CO2 (Suzuki et al. 1986(a), 1986(b), Beal et al. 1994, Tamime and Robinson 2007, Angelov et al. 2009). On the other hand, L. bulgaricus possesses more proteolytic enzymes than S. thermophilus (Rajagopal and Sandine 1990, Tamime and Robinson 2007). In this way, L. bulgaricus stimulates the growth of S. thermophilus by releasing amino acids like glycine and histidine, and short peptides into the growth medium (Tamime and Robinson 2007, Angelov et al. 2009). Although the effect of the association of these bacteria is often positive, it can also be neutral or detrimental depending on the bacterial strains employed, the type of milk, the method used to heat the milk, and the temperature of milk (Tamime and Robinson 2007, Angelov et al. 2009). Whey is the byproduct of cheese manufacturing plants and a cheap nutritious material. It contains all of the lactose, non-protein nitrogen, organic acids, ash, and water-soluble vitamins of the milk (Tamime and Robinson 2007). Whey has been used as a carbon source to produce lactic acid bacteria and lactic acid (Beal et al. 1989, Bassi et al. 1991, Parente and Zottola 1991, Chiarini et al. 1992, Jokar and Karbassi 2009, Aghababaie et al. 2014). The proto-cooperation between S. thermophilus and L. bulgaricus may be different in whey medium which is enriched only by yeast extract. Mathematical models are powerful tools in simulation and control of such dynamic processes. Various aspects of the metabolism and growth of these bacteria in single strain culture have been reported in previous studies (Beal et al. 1989, Beal and Corrieu 1998). Several models have been proposed to formulate the effect of 5
factors, like temperature, pH, concentration of carbon, nitrogen sources, and the main inhibitory metabolite (i.e. lactic acid), in the kinetic modeling of L. helveticus (Schepers et al., 2002b), L. deibrueckii (Luedeking and Piret, 2000), L. casei (Alvarez et al., 2010), and L. bulgaricus (Venkatesh et al. 1993, Gadgil and Venkatesh 1996, Luedeking and Piret 2000, Schepers et al. 2002b, Alvarez et al. 2010). Despite the abundance of mixed cultures in nature, there are limited number of researches on kinetics of these systems mainly due to the complexity of their dynamics and difficulty of their analysis and control (Katoh et al. 1999). In one study, a model was developed for this system with the assumption that no interaction exists between the two bacteria (Sodini et al. 2000). In another attempt, the Volterra equation for competitive growth was used to model the mixed culture of the two bacteria in a batch fermentation without pH control (Berkman et al. 1990). The model has successfully covered experimental data; however, it contains no term to describe the dependency of growth rate on various factors such as temperature, pH, and medium composition. In the present study, a kinetic model was developed for the growth kinetics of L. bulgaricus and S. thermophilus in co-culture. To overcome the shortages of the abovementioned models, both environmental effects, i.e. temperature and pH , and interaction of the microorganisms are considered in this model. The co-culture model was an extension of the single strain kinetic model of S. thermophilus and L. bulgaricus which was validated in a previous study (Aghababaie et al. 2014). In this co-culture model, the effect of each bacterium on the other was considered in different terms. Response surface methodology (RSM) was implemented to investigate the effect of pH and temperature on the growth, lactic acid production, total population, and final percentage of S. thermophilus in the co-culture of S. 6
thermophilus and L. bulgaricus. The coefficients of the co-culture model were determined and the model was validated for the co-culture experiments. 2.
Theory
In a previous study by the authors, the simple Malthusian growth kinetic model was applied in combination with the terms that describe the influence of various factors (Aghababaie et al. 2014). The effect of carbon and nitrogen substrates, temperature, pH, and dissociated and undissociated forms of lactic acid were considered in the single strain kinetic model. These expressions are depicted in Table 1. Parameters of these expressions were estimated previously in the study of single strain kinetic modeling of these strains (Aghababaie et al. 2014). This kinetic model for the growth of bacterium i was described as follows:
dXi dt
i i i i i imax fTi f pH fScfSn f Laf HLaXi
(1)
In order to describe the co-culture kinetic model, fji was inserted into the single strain kinetic model to describe the effect of one bacterium on the other. dXim i i i i i imax fTi f pH fScfSn f Laf HLaf ji Xim dt
(2)
In Eq (2), fij is the effect of bacterium j on specific growth rate of bacterium i. To comply with the proto-cooperation effect, it is assumed that bacterium j produces metabolites which eventually stimulate the growth of the other bacterium. In single strain culture model, this term was equal to 1.0. Table 1. 2.1. Effect of L. bulgaricus on S. thermophilus (fSL) Short peptides and amino acids which have been released due to the proteolytic activity of L. bulgaricus in whey proteins, would stimulate the growth of S.
7
thermophilus (Tamime and Robinson 2007, Angelov et al. 2009). Accumulation rate of these metabolites was determined as below:
dC pep dX mL dX mS L g pep hpep X m q pep dt dt dt
(3)
The effect of these metabolites on the growth rate of S. thrmophilus could be described in the Monod type model as follows: f LS Z
C pep
(4)
C pep K pep
2.2. Effect of S .thermophilus on L. bulgaricus ( f SL ) S. thermophilus produces lactic and formic acids and carbon dioxide which reduces the pH of the medium and makes it suitable for the growth of L. bulgaricus in milk (Tamime and Robinson 2007, Angelov et al. 2009). While pH was constant during the fermentation, this effect is negligible in this study. However, the effect of dissociated and undissociated lactic acid concentrations was considered in the model. Furthermore, formic acid and carbon dioxide stimulate the growth of L. bulgaricus through other mechanisms. The accumulation rate of formic acid could be estimated by the following equation:
dCf dXSm dX Lm S gf hf Xm qf dt dt dt
(5)
Formic acid is consumed by L. bulgaricus while some portion of CO2 transfers to gas phase and some changes to other forms of CO2 (HCO-3, HCO-2), based on the pH of the fermentation. In this issue, the effect of carbon dioxide was negligible. Thus, the effect of S. thermophilus on L. bulgaricus ( f SL ) could be described by the concentration of formic acid in Monod type model as below:
f SL W
Cf Cf K f
(6) 8
2.3. Lactic acid production rate The Luedeking-Piret equation was applied for describing lactic acid production rate (rp) in co-culture as follows (Luedeking and Piret 2000): rp
dP dXSm dX Lm aS bSXSm a L b L X Lm dt dt dt
(7)
2.4. Substrates consumption rates Carbon substrate is converted to lactic acid, biomass of both S. thermophilus and L. bulgaricus, and trace amounts of secondary metabolites. The rate of carbon substrate consumption is equal to the sum of the product and biomass formation rates (Venkatesh et al. 1993) and is obtained by the following equation:
dSc dX mS dX mL dP 1.19 1.19 0.95 i dt dt dt dt
(8)
The usable nitrogen content in yeast extract is converted into biomass (Aghababaie et al. 2014). The rate of nitrogen substrate consumption is given below:
dSn dXSm dX Lm SnM LnM dt dt dt
(9)
2.5. Model simulation The simulating mathematical model for single strain culture is constructed by combining the abovementioned set of governing differential equations:
9
1 0 1.19 S a S nM q pep g f
3.
0 1 1.19 aL L nM
g pep qf
0 0 0 0 1 0.95 0 1 0 0 0 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 1 0
dX mS dt dX mL S S S S S S S S S f f f f f f f X 0 dt max T pH La HLa S N SC L m 0 dSc L f L f L f L f L f L f L f LX L 0 dt max T pH La HLa S N SC S m 0 dPi 0 S S b X m b L X mL dt 0 dS n 0 0 dt hpep X mL 1 dC pep h f X mS dt dC f dt
(10)
Materials and methods
3.1. Microorganism and culture media Single strain batch cultures of Streptococcus thermophilus and Lactobacillus bulgaricus in whey and yeast extract medium with different pH and temperatures have been previously described (Aghababaie et al. 2014). Streptococcus thermophilus PTCC 1738 (ATCC 19258) was obtained from microbial collection of the Iranian Research Organization for Science and Technology. Lactobacillus delbrockii ssp bulgaricus was isolated from a traditional yogurt. Cultures were prepared from frozen stocks at 1% (v/v), and incubated for 18h at 40 °C. In coculture experiments, initial population ratio of S. thermophilus to total population (Xs/XT) in all of the experiments was considered as 50%. Medium composition in co-culture experiments were similar to that in single strain culture’s which was described in details previously (Aghababaie et al. 2014). The medium contained a sterile solution of 100 g/L whey and 10 g/L yeast extract in a 1.0 liter in-house manufactured bioreactor.
10
3.2. Design of experiments Central Composite, Uniform Precision Design of RSM was applied with 12 runs in order to estimate the effects of pH and temperature on the growth and lactic acid production of S. thermophilus and L. bulgaricus in co-culture. This design included 4 factorials, 4 axials, and 4 center points that were considered with different pH and temperature levels for co-culture experiments (Table 2). Analysis of variance was performed for maximum cell population (X max) and maximum specific growth rate (µmax) of each bacterium, total population of co-culture (XT), ratio of maximum S. thermophilus concentration to total population (X s/XT), and total produced lactic acid. Optimum pH and temperature for the growth of these bacteria were estimated by RSM analysis. Analysis was performed using SAS software (version 9.0; SAS Institute Inc., Cary, NC, USA). Table 2. 3.3. Analysis Lactic acid production rate in the fermenter was determined by the intermittent addition of 5N NaOH at appropriate time intervals using a peristaltic pump (Beal and Corrieu 1995). The fermenter was sampled at 30-minute intervals and placed in
the refrigerator (Beal et al. 1989). M17 and MRS agar mediums were used for enumeration of S. thermophilus and L. bulgaricus, respectively, which were used for CFU counting of co-culture during fermentation (Berkman et al. 1990). The microbial growth was measured by microscopy using a Thoma counting chamber with 0.02 mm depth according to their different morphology (Aghababaie et al. 2014). The biomass average specific dry weight (g/cell) was determined by measuring the weight of a dried sample containing a predetermined number of the bacterial cells cultivated in single strain cultures. Initial concentration of lactose in 11
whey solution, as determined by colorimetric dinitrosalicylic acid (DNS) method, was about 60 g/l. Lactose concentration during fermentation has a linear correlation with the produced lactic acid concentration (Beal and Corrieu 1995). To estimate the molar concentration of lactose during the fermentation the following equation (Beal and Corrieu 1995) was used:
CSC [CSC0 / 342 (m / 90).(CP )] 342
(11)
In this equation, m was about -0.54 and -0.61 for S. thermophilus and L. bulgaricus, respectively, in single strain cultures and -0.57 for their co-culture. Here, Csc0 was the initial concentration of lactose (Beal and Corrieu 1995). The yield of biomass on nitrogen substrate (YSNx) for some lactic acid bacteria is about 1.0 (g biomass/g nitrogen) (Nielsen et al. 1991, Schepers et al. 2002b).The nitrogen substrate concentration throughout the co-culture fermentation can be calculated through the linear equation:
CSN CSN0 (1 / YSNx )( X i )
(12)
where, CSN was the initial concentration of yeast extract. 3.4. Parameter estimation and model solution The single strains parameters have been estimated previously using SBToolbox2 on Matlab 7.12.0. (R2011a,The MathWorks Inc., Natick, MA, USA) (Aghababaie et al. 2014). The same values were used for co-culture simulation, and therefore, only the parameters of f SL and f LS , i.e. parameters of equations 3 to 6, were estimated in the present study. Particle swarm algorithm was applied in SBToolbox2 with its default options to estimate the co-culture model parameters (Vaz and Vicente 2007, 2009, Henkel et al. 2011). Experimental results related to biomass of S. thermophilus and L. bulgaricus, lactic acid, nitrogen, and carbon substrate concentrations of each experiment were the input data for SBToolbox2. 12
The particle swarm algorithm minimizes the sum of quadratic differences between measurements and simulations, and reports the minimum function which shows the appropriateness of fitting (Henkel et al. 2011). The closer the minimum function is to zero the better the fitting. Eq. (10) was solved using ode23 function of Matlab based on the Trapezoidal rule to compare the experimental data and predicted model. 4.
Results and discussion
4.1. Statistical analysis of experimental results According to the RSM analyses of S. thermophilus and L. bulgaricus single strain cultures, pH and temperature had a significant effect on the growth of these bacteria at the examined range. Optimum pH and temperature were 7 and 42.8 °C for single strain growth of S. thermophilus, and 5.2 and 44 °C for single strain growth of L. bulgaricus, respectively. RSM analysis of co-culture experiments showed that maximum population (Xmax) of each bacterium and total produced lactic acid in the bioreactor depended on the pH and temperature of the fermentation. Total population (XT) and ratio of maximum S. thermophilus population to total population (Xs/XT) were pH and temperature dependent. Thus, the desired ratio can be obtained by controlling the pH and temperature of the fermentation. Optimum pH and temperature, in order to attain maximum total population (XT) alongside the desired ratio of 83% (Xs/XT), were 6 and 46 °C, respectively. However, optimum pH and temperature for obtaining maximum population of each bacterium were different. In the co-culture experiments, optimum pH values were in the range of 6.10-6.40 for the growth of S. thermophilus, and in the range of 5.70-6.10 for the growth of 13
L. bulgaricus. Optimum temperatures were about 42 °C for both bacteria in the coculture experiments. The optimum growth conditions of each bacterium in coculture are different from that of single strain culture (Aghababaie et al. 2014). In the co-culture model, pH and temperature will affect the growth of each bacterium ,and eventually, influence the metabolite productions and microbial growth. 4.2. Co-culture vs. pure culture According to the RSM results, optimum pH and temperature to attain the maximum total populations of these bacteria in co-culture were 6.1 and 42 °C, respectively. In the optimum conditions, the maximum populations of S. themophilus and L. bulgaricus in co-culture were 8.3 and 39.5 times more than that of their single strain cultures. Thus, the presence of S. thermophilus is more beneficial for L. bulgaricus than vice versa. Total lactic acid produced in co-culture was 1.4 times that of single strain cultures. Total population in co-culture was 10 times the of sum of populations of single strain cultures. Furthermore, it should be mentioned that by producing the starters in co-culture, half of the medium would be used compared with two batches of single strain cultures. Therefore, medium, energy, and time will be saved. 4.3. Effect of L. bulgaricus on S. thermophilus in co-culture According to the results of single strain and co-culture experiments of S.thermophilus, it was observed that the growth of S. thermophilus in co-culture experiments was not much higher than that of S. thermophilus in single strain cultures (Aghababaie et al. 2014). Thus, it is revealed that the effect of L. bulgaricus on S. thermophilus depends on the medium composition. Since the whey permeate lacks milk proteins, the proteolitic activity of L.bulgaricus was not useful in the whey based mediums. 14
4.4. Effect of S. thermophilus on L. bulgaricus in co-culture The presence of S. thermophilus enhanced the growth of L. bulgaricus evident in comparison with that of single strain (Aghababaie et al. 2014). It is known that S. thermophilus grows faster than L. bulgaricus and supports the growth of L. bulgaricus mainly by producing lactic and formic acid. Moreover, S. thermophilus assimilates oxygen faster, and thus, creates favorable conditions for L. bulgaricus growth (Angelov et al., 2009). 4.5. Estimated values of parameters Estimated values for the co-culture parameters is presented in Table 2, along with that of single strain culture parameters which were determined in single strain modeling (Aghababaie et al. 2014). Minimum function reported for this set of estimated parameters was about 0.06. The minimum function is a measure of fitting error, and so, this small quantity represents high goodness of fit resulted from the values depicted in Table 3. By setting fjis as equal to 1.0, the single strain culture model is obtained. In the case of co-culture growth, this term will increase with time which demonstrates the effect of produced metabolites on the other bacterium during the fermentation. Table 3. 4.6. co-culture kinetic model validation Validity of the kinetic model for single strain culture, i.e. Eq.(1), has been tested against experimental data and good agreements have been observed between the experimental data and model predictions for the growth and lactic acid production of L. bulgaricus and S. thermophilus in single strain cultures (Aghababaie et al. 2014).
15
Practiced experiments of co-cultures were simulated by solving Eq. (10) with the parameter values shown in the Table 3. Figs. 1 and 2 depicts the experimental and model prediction of S. thermophilus and L. bulgaricus growth and lactic acid production trends. The concentration of the metabolites can also be calculated by the model simulation. In all the considered cases, there was a good agreement between the experimental data and simulated trends. This confirms the validity of the model, and especially, the way the cooperation of the two bacteria was formulated. Fig. 1 Fig. 2 While few researches have been performed on culture modeling, this model would be useful for other symbiotic relationships. The previous mixed culture model which was presented for S. thermophilus and L. bulgaricus by Berkman et al. (1990), was less mechanistic than the current model, since the effect of each bacterium on the other was considered as a function of the bacterium biomass instead of its influencing metabolite. The ratio between S. thermophilus and L. delbrueckii subsp. bulgaricus in the yogurt starter culture influences the organoleptic properties of the fermented product. A ratio of 1:1 (chain: chain) of S. thermophilus to L. bulgaricus is used for the production of conventional yogurt in many parts of the world. As mentioned before, this ratio corresponds to 5:1 ratios of single cell numbers of these two bacteria. In Some countries, the statutory regulations may stipulate the use of this ratio (Tamim and Robinson, 2007). However, a ratio of 40:60 can be used for the production of sharp flavored yoghurt, while for milder flavored yoghurt a ratio of 60:40 can be used (Tamim and Roninson, 2007). Therefore, adjustment of the 16
customer desired ratio is important and the developed model can help to predict and control the mixed culture process to attain any predetermined ratio of the two bacteria in the produced starter. 5.
Conclusion
In the present study, co-culture of yogurt starter species in whey based medium was investigated. The results showed that pH and temperature have significant effect on the growth, lactic acid production, and final population and percentage of S. thermophilus. Optimum pH and temperature to obtain the maximum population and desired ratio of 5:1 of S. thermophilus to L. bulgaricus were about 6.4 and 46 °C, respectively. In the whey based medium the effect of S. thermophilus on the growth of L.bulgaricus was more considerable than vice versa. This reveals that the proto-cooperation between S. thermophilus and L. bulgaricus depends on the medium composition and it is different in whey in comparison with milk. A kinetic model was developed to predict the behavior of co-culture growth of S. thermophilus and L. bulgaricus as a function of pH, temperature, carbon substrate, nitrogen substrate, lactic acid concentration, and their interactions. This model was capable of predicting bacterial growth at different pH and temperatures in the examined ranges in single strain and co-culture, and is useful for simulating and controlling the fermentation process of these bacteria. It could be extended for simulating growth of the bacteria in milk and in varying pH conditions. The developed model can pave the way for future studies in different mixed culture modeling efforts. 6.
Acknowledgments
This study was financially supported by the Isfahan Center for Research on Agricultural Science and Natural Resources, and the University of Isfahan. 17
7.
References
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Beal, C., Louvet, P. & Corrieu, G. (1989). "Influence of controlled pH and temperature on the growth and acidification of pure cultures of Streptococcus thermophilus 404 and Lactobacillus bulyaricus 398." Applied Microbiology and Biotechnology, 32: 148-154. Beal, C., Spinnler, H.E. & Corrieo, G. (1994). "Comparison of growth, acidification and productivity of pure and mixed cultures of Streptococcus salivarius subsp, thermophilus 404 and Lactobacillus delbrueckii subsp, bulgaricus 398." Applied Microbiology and Biotechnology, 41: 95-98. Berkman, T., Bozolu, T.F. & Özilgen, M. (1990). "Mixed culture growth kinetics of Streptococcus thermophilus and Lactobacillus bulgaricus." Enzyme and Microbial Technology 12(2): 138-140. Chiarini, L., Mara, L. & Tabacchioni, S. (1992). "Influence of growth supplements on lactic acid production in whey ultrafiltrate by Lactobacillus helveticus." Appl Microbiol Biotechnol 36: 461-464. Driessen, F.M., Kingma, F. & Stadhouders, J. (1982). "Evidence that
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bulgaricus in yoghurt is stimulated by carbon dioxide produced by Streptococcus thermophilus." Neth Milk Dairy J 36(135-144). Gadgil, C.J. & Venkatesh, K.V. (1996). "Structured Model for Batch Culture Growth of Lactobacillus bulgaricus." Journal of Chemical Technology and Biotechnology, 68(1): 8993. Henkel, S., Nägele, T., Hörmiller, I., Sauter, T., Sawodny, O., Ederer, M. & Heyer, A.G. (2011). "A systems biology approach to analyse leaf carbohydrate metabolism in Arabidopsis thaliana " EURASIP Journal on Bioinformatics and Systems Biology, 2: 1-10. Jokar, A. & Karbassi, A. (2009). "Determination of Proper Conditions for the Production of Crude Beta-galactosidase Using Lactobacillus delbrueckii ssp. bulgaricus." Journal of Agricaltural Science and Technology, 11: 301-308. Katoh, T., Yuguchi, D., Yoshii, H., Shi, H. & Shimizu, K. (1999). "Dynamics and modeling on fermentative production of poly (β-hydroxybutyric acid) from sugars via
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lactate by a mixed culture of Lactobacillus delbrueckii and Alcaligenes eutrophus." J Biotechnol 67(2-3): 113-134. Luedeking, R. & Piret, E.L. (2000). "A kinetic study of the lactic acid fermentation. Batch process at controlled pH." Biotechnology and Bioengneering, 67(6): 636 - 644. MacBean, R.D., Hall, R.J. & Linklater, P.M. (1979). "Analysis of pH-stat continuous cultivation and the stability of the mixed fermentation in continuous yoghurt production." Biotechnology and Bioengneering, 21: 1517-1541. Moon, N.J. & Reinhold, G.W. (1976). "Commensalism and competition in mixed cultures of Lactobacillus bulgaricus and Streptococcus thermophilus." Journal of milk and food Technology, 39: 337-341. Nielsen, J., Nikolajsen, K. & Villadsen, J. (1991). "Structured modeling of microbial system:IIExperimental verification of structured lactic acid fermentaion model." Biotechnology and Bioengneering, 38: 11-23. O'Leary, V.S. & Woychik, J.H. (1976). "Utilization of lactose, glucose and galactose by a mixed culture of Streptococcus thermophiIus and Lactobacillus bulgaricus in milk treated with lactase enzyme." Applied Environmental Microbiology, 32: 89-94. Parente, E. & Zottola, E.A. (1991). "Growth of Thermophilic Starters in Whey Permeate Media." Jouranl of Dairy Science, 74: 20-28. Pette, J.W. & Lolkema, H. (1950). "Yoghurt. I. Symbiosis and antibiosis in mixed culture of Lactobacillus bulgaricus and Streptococcus therrnophilus." Netherland Milk and Dairy Journal, 4: 197-208. Rajagopal, S.N. & Sandine, W.E. (1990). "Associative growth and proteolysis of Streptococcus thermophilus and Lactobacillus bulgaricus in skim milk." Journal of Dairy Science, 69: 2558-2568. Schepers, A.W., Thibault, J. & Lacroix, C. (2002b). "Lactobacillus helveticus growth and lactic acid production during pH-controlled batch cultures in whey permeate/yeast extract medium. Part II: kinetic modeling and model validation." Enzyme Microbiology and Technology, 30(2): 187-194. 20
Sodini, I., Latrille, E. & Corrieo, G. (2000). "Identification of interacting mixed cultures of lactic acid bacteria by their exclusion from a model predicting the acidifying activity of non-interacting mixed cultures." Applied Microbiology and Biotechnology, 54: 715-718. Suzuki, I., Kato, S., Kitada, T., Yano, N. & Morichi, T. (1986(a)). "Growth of Lactobaci//us bulgaricus in Milk. 1.Cell Elongation and the Role of Formic Acid in Boiled Milk." Journal of Dairy Science, 28: 311-320. Suzuki, I., Kato, S., Kitada, T., Yano, N. & Morichi, T. (1986(b)). "Growth o f Lactobacillus bulgaricus in Milk. 2. Characteristics of Purine Nucleotides, Pyrimidine Nucleotides, and Nucleic Acid Synthesis." Journal of Dairy Science, 69: 971-980. Tamime, A.E. & Robinson, R.K. (2007). Tamime and Robinson's Yoghurt Science and technology. New York, CRC press. Vaz, A.I.F. & Vicente, L.N. (2007). " A particle swarm pattern search method for bound constrained global optimization." Journal of Global Optimization, 39: 197-219. Vaz, A.I.F. & Vicente, L.N. (2009). "PSwarm: a hybrid solver for linearly constrained global derivative-free optimization." Optimization Methods and Software, 24(4-5). Venkatesh, K.V., Okos, M.R. & Wankat, P.C. (1993). "Kinetic Model of Growth and Lactic Acid Production from Lactose by Lactobacillus bulgaricus." Process Biochemestry, 28: 231-241.
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Tables
Table 1. Functions of the kinetic model described previously for single strain cultures
Equation
Function
e
fT
Function of temperature (fT)
E a RT (
1 Ae
f pH
Function of pH (fpH)
G a ) RT
C1 (pHopt pH) 2 C 2 (pHopt pH) 2 C3
Function of carbon substrate (fSc)
fSC
Csc Csc K c
Function of nitrogen substrate (fSN)
fSN
CSN CSN K N
Function of lactate (fLa)
f La ek i .CLa
Function of lactic acid (fHla)
1 f Hla K p (C Hla K Hla ) 1 e
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Figure
Figures
(a)
(b)
(c)
(d) Fig 1. Experimental data (symbols) and model prediction (lines) - biomass and lactic acid vs. time for co-culture of S. thermopnilus and L. bulgaricus (a) 38.0°C and pH=5.70 (b) 38.0°C and pH =6.50 (c) 46.0 °C and pH=5.70 (d) 46.0 °C and pH=6.50
(a)
(b)
(c)
(d) Fig 2. Experimental data (symbols) and model prediction (lines) - biomass and lactic acid vs. time for co-culture of S. thermopnilus and L. bulgaricus; (a) 36.3 °C and pH=6.10; (b) 42.0 °C and pH=5.53 ;(c) 42.0 °C and pH= 6.66 ;(d) 42.0 °C and pH=6.10
Table 2. Experimental conditions based on RSM for batch cultures
RUN 1 2 3 4 5 6 7 8 9 10 11 12
Coded values L. bulgaricus Tc pHT(°C) PH c -1 -1 40.0 4.90 -1 1 40.0 6.50 1 -1 48.0 4.90 1 1 48.0 6.50 -1.41 0 38.3 5.70 1.41 0 49.6 5.70 0 -1.4144.0 4.56 0 1.4144.0 6.83 0 0 44.0 5.70 0 0 44.0 5.70 0 0 44.0 5.70 0 0 44.0 5.70
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S. thermophilus Co-culture T (°C) pH T (°C) pH 36.0 5.7038.0 5.70 36.0 7.3038.0 6.50 44.0 5.7046.0 5.70 44.0 7.3046.0 6.50 34.3 6.5036.3 6.10 45.6 6.5047.6 6.10 40.0 5.3642.0 5.53 40.0 7.6342.0 6.66 40.0 6.5042.0 6.10 40.0 6.5042.0 6.10 40.0 6.5042.0 6.10 40.0 6.5042.0 6.10
Table 3. Parameters of the proposed model Parameter μ max,L AL E aL GaL pHoptL C1L C2L C3L KcL K NL KpL KLaL kHLaL aL bL δn,L μ max,S AS E aS GaS pHoptS C1S C2S C3S KcS K NS KpS KLaS kHLaS aS bS δns gf hf qf gp hp qp Kf Kpep Z W
value source 1.95 SSC of L. bulgaricus (Aghababaie et al. 2014) 1.9E+6 SSC of L. bulgaricus (Aghababaie et al. 2014) 80 SSC of L. bulgaricus (Aghababaie et al. 2014) 55430 SSC of L. bulgaricus(Aghababaie et al. 2014) 5.249 SSC of L. bulgaricus(Aghababaie et al. 2014) 6.64 SSC of L. bulgaricus (Aghababaie et al. 2014) 69.32 SSC of L. bulgaricus(Aghababaie et al. 2014) 2.77 SSC of L. bulgaricus (Aghababaie et al. 2014) 2.48 SSC of L. bulgaricus (Aghababaie et al. 2014) 124.7 SSC of L. bulgaricus (Aghababaie et al. 2014) 0.4979 SSC of L. bulgaricus (Aghababaie et al. 2014) 0.44 SSC of L. bulgaricus (Aghababaie et al. 2014) 0.00001 SSC of L. bulgaricus (Aghababaie et al. 2014) 0.7 SSC of L. bulgaricus (Aghababaie et al. 2014) 0.6 SSC of L. bulgaricus (Aghababaie et al. 2014) 1.08 SSC of L. bulgaricus (Aghababaie et al. 2014) 1.177 SSC of S. thermophilus (Aghababaie et al. 2014) 1.2E+6 SSC of S. thermophilus (Aghababaie et al. 2014) 130 SSC of S. thermophilus (Aghababaie et al. 2014) 52160 SSC of S. thermophilus (Aghababaie et al. 2014) 6.87 SSC of S. thermophilus (Aghababaie et al. 2014) 45.42 SSC of S. thermophilus (Aghababaie et al. 2014) 11.25 SSC of S. thermophilus (Aghababaie et al. 2014) 0.123 SSC of S. thermophilus (Aghababaie et al. 2014) 0.000001 SSC of S. thermophilus (Aghababaie et al. 2014) 253.1 SSC of S. thermophilus (Aghababaie et al. 2014) 52.86 SSC of S. thermophilus (Aghababaie et al. 2014) 0.3259 SSC of S. thermophilus (Aghababaie et al. 2014) 0.0444 SSC of S. thermophilus (Aghababaie et al. 2014) 1.54 SSC of S. thermophilus (Aghababaie et al. 2014) 0.52 SSC of S. thermophilus (Aghababaie et al. 2014) 0.98 SSC of S. thermophilus (Aghababaie et al. 2014) 1.54 Co-culture (this study) 2 Co-culture (this study) 2 Co-culture (this study) 0.21 Co-culture (this study) 1.1 Co-culture (this study) 2 Co-culture (this study) 2 Co-culture (this study) 5 Co-culture (this study) 180 Co-culture (this study) 50 Co-culture (this study)
SSC: Single Strain Culture
24
Highlights A co-culture growth kinetic model was developed by the extension of single strain models. Influence of each bacterium on the other was considered in the co-culture model. The model parameters were estimated with the use of particle swarm algorithm. The model was able to simulate experimental data properly.
25