Developing a detailed kinetic model for the production of yogurt starter bacteria in single strain cultures

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Developing a detailed kinetic model for the production of yogurt starter bacteria in single strain cultures Marzieh Aghababaie a , Morteza Khanahmadi b , Masoud Beheshti c,∗ a

Biotechnology Department, Faculty of Advanced Sciences and Technologies, University of Isfahan, Isfahan, Iran Agricultural Engineering Department, Isfahan Center for Research on Agricultural Science and Natural Resources, Isfahan, Iran c Chemical Engineering Department, Engineering Faculty, University of Isfahan, Isfahan, Iran b

a b s t r a c t Streptococcus thermophilus and Lactobacillus bulgaricus are the most common yogurt starter cultures used in the dairy industry. Generally, they are produced by single strain fermentation and then mixed together in appropriate proportions for the purpose of yogurt production. In the present study a kinetic model was developed for the growth and lactic acid production by these two bacteria in pH-controlled single strain batch cultures and whey based medium. The model is a function of pH, temperature, biomass, lactic acid, carbon, and nitrogen substrate concentrations. A four-parameter function was used to describe the effect of pH on the growth of each bacterium. Moreover, a modified Arrhenius law was applied in the model to describe the temperature effect. Response surface methodology was implemented to design the experiments in order to estimate the effect of pH and temperature on bacterial growth. The model was validated on a set of 12 experiments for each bacterium. © 2014 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Streptococcus thermophilus; Lactobacillus bulgaricus; Kinetic modeling; Single strain culture; Lactic acid; Batch fermentation

1.

Introduction

Streptococcus salivarius ssp. thermophilus and Lactobacillus delbrueckii ssp. bulgaricus are homofermentative lactic acid bacteria and the traditional starter cultures in yogurt and cheese production. They have an interaction, named proto-cooperation, in yogurt, which is a symbiotic relationship and combined metabolism with positive effects on the fermented product (Pette and Lolkema, 1950; Angelov et al., 2009). Generally, they are produced by single strain fermentation and then mixed together in appropriate proportions for the purpose of yogurt production (Beal et al., 1989; Beal and Corrieu, 1998). The starter culture production in mixed culture mode is less costly, although controlling the process to achieve the favorable ratio of these bacteria is difficult. Moreover, these bacteria have the ability to produce lactic acid, which is an important ingredient used in the food, chemical, textile, pharmaceutical, and other industries. In recent years, lactic acid has been used

as a monomer for the production of biodegradable (polylactic) polymer (Datta et al., 1995; Auras et al., 2010; Mozzi et al., 2010). Effect of various factors on the metabolism and growth of these bacteria in single strain culture have been investigated in previous studies (Beal et al., 1989; Beal and Corrieu, 1998). Temperature and pH are the dynamic operating factors that can be continuously monitored and easily adjusted. Therefore, they could be means by which the trend of growth and product formation of lactic acid bacteria can be effectively controlled. Medium composition could not be controlled in batch fermentation and so varies during the fermentation and impress bacterial metabolism. Due to significant contribution of kinetic modeling in understanding, designing and controlling the fermentation processes, several models have been proposed to formulate the effect of factors on the growth kinetics of the lactic acid bacteria. The mostly investigated factors include temperature, pH, concentration of carbon and nitrogen sources, and the main inhibitory metabolite, i.e. lactic acid. Kinetic

∗

Corresponding author. Tel.: +98 3117934013; fax: +98 3117934031. E-mail addresses: maz [email protected] (M. Aghababaie), [email protected] (M. Khanahmadi), [email protected] (M. Beheshti). Received 9 April 2014; Received in revised form 22 September 2014; Accepted 26 September 2014 http://dx.doi.org/10.1016/j.fbp.2014.09.007 0960-3085/© 2014 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Please cite this article in press as: Aghababaie, M., et al., Developing a detailed kinetic model for the production of yogurt starter bacteria in single strain cultures. Food Bioprod Process (2014), http://dx.doi.org/10.1016/j.fbp.2014.09.007

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Nomenclature A a b C1 C2 C3 CHLa CLa CP CSC CSN Ea fji Ga Kc KHla KLa KN KP m R pHopt T X  max YSNx ın

constant in temperature function non-growth associated production coefficient for lactic acid (g lactic acid/g biomass) growth associated production coefficient for lactic acid (g lactic acid/(g biomass h)) first coefficient of effect of pH on growth rate second coefficient of effect of pH on growth rate third coefficient of effect of pH on growth rate concentration of undissociated lactic acid (g/L) concentration of lactate ion (g/L) concentration of product (lactic acid) (g/L) concentration of carbon substrate (g/L) concentration of nitrogen substrate (g/L) activation energy of effect of temperature on growth (kJ/gmol) functions that demonstrated the effect of parameter j on the growth of bacterium i free energy of effect of temperature on growth (kJ/gmol) Monod constant for carbon source (g/L) undissociatted lactic acid inhibition parameter (g/L) lactate inhibition parameter (L/g) Monod constant for nitrogen source (g/L) second lactic acid inhibition parameter (L/g) coefficient of proportionality (mol lactose consumed/mol lactic acid produced) universal gas constant (8.314 kJ/gmol/K) optimum pH in the function of pH temperature (K) biomass concentration (g/L) specific growth rate of bacteria (1/h) maximum specific growth rate of bacteria in single strain culture (1/h) theoretical bacteria yield on nitrogen substrate (g biomass/g nitrogen) biomass yield on nitrogen substrate (g biomass/g nitrogen)

Superscripts (i) L L. bulgaricus S. thermophilus S Subscripts of functions (j) effect of temperature T pH effect of pH effect of carbon substrate C N effect of nitrogen substrate effect of lactate concentration La effect of lactic acid concentration Hla

modeling of Lactococcus lactis (Åkerberg et al., 1998), Lactococcus helveticus (Schepers et al., 2002b), L. delbrueckii (Luedeking and Piret, 2000), Lactobacillus casei (Alvarez et al., 2010), and L. bulgaricus (Venkatesh et al., 1993; Gadgil and Venkatesh, 1997) have been attempted in this regard. The Luedeking–Piret equation, which correlates the instantaneous acid formation rate to the instantaneous bacterial growth rate and the bacterial concentration, has been applied in the above mentioned studies. The growth and non-growth associated parameters of the Luedeking–Piret equation have been determined for different pH values (Gadgil and Venkatesh, 1997) and for different medium

compositions (Schepers et al., 2002a). A structured model was developed for L. bulgaricus with the assumption that a key enzyme controls the bacterial growth (Gadgil and Venkatesh, 1997). Additionally, a Monod type expression with a linear lactate inhibition, substrate inhibition term, and an exponential term for undissociated lactic acid was applied for the growth of L. bulgaricus (Venkatesh et al., 1993). In this model, two different terms were used to determine the impact of lactate and undissociated lactic acid on bacterial growth (Venkatesh et al., 1993). Del Nobile et al. (2003) developed a stochastic-deterministic model to describe the entire cell growth curve of L. bulgaricus. Even so, a simple model has been proposed for S. thermophilus where the values of coefficients were regarded as a measure of the extent of antibiotic effect (Yondem et al., 1989). Ishizaki et al. (1989) applied a Monod equation for S. thermophilus by assuming lactic acid to be an uncompetitive inhibitor. A number of models have also been proposed for the growth of exo-polysaccharide producing strains (Degeest and De Vuyst, 1999; Vaningelgem et al., 2004). All of the above mentioned works and most of other lactic acid bacteria models (Bouguettoucha et al., 2011) have focused on one or a few effective factors on the growth kinetic model. Thus, a more complete kinetic model is presented here to describe the L. bulgaricus and S. thermophilus growth and lactic acid production rates in terms of pH and temperature, dissociated and undissociated forms of lactic acid, and carbon and nitrogen substrates in single strain cultures. First of all, response surface methodology (RSM) was implemented to evaluate the effect of pH and temperature on the growth and lactic acid production of these bacteria in single strain cultures, and predict the dependency of the Luedeking–Piret parameters on pH and temperature. Afterwards, experimental data were used to estimate the parameters of the model, and to validate the model. In the present work, unlike many other modeling efforts, effect of each factor was considered in this model as an independent function which alleviated analyzing the effect of each factor on the growth of these bacteria independently. Furthermore, the impact of extra factors such as presence of another microorganism in mixed culture can be inserted in this model by adding an independent function with no need of changing the other ones. This model was applied for single strain culture of these bacteria and is ready to be modified for mixed culture modeling.

2.

Theory

L. bulgaricus and S. thermophilus are the lactic acid bacteria that convert lactose to glucose and galactose using the enzyme ␤-galactosidase. Glucose and galactose are subsequently converted to pyruvate and ATP through the glycolytic pathway, and then, pyruvate is converted to lactic acid (Venkatesh et al., 1993). In the present study, the simple exponential Malthusian growth rate kinetic model was applied along with the terms that describe the effect of each factor. The effects of carbon and nitrogen substrates, temperature, pH, and dissociated and undissociated forms of lactic acid were implemented in the model according to Eq. (1). dXi i i i fCi fNi fLa fHLa Xi = imax fTi fpH dt

(1)

where fji is a one variable function that express the impact of factor j on growth of bacterium i.

2.1.

Function of temperature (fT )

The Arrhenius Law can describe the effect of temperature on the specific reaction rate constant in chemical reactions, although it is not appropriate to describe the dependence of bacterial growth on temperature (Ratkowsky et al., 1982). A

Please cite this article in press as: Aghababaie, M., et al., Developing a detailed kinetic model for the production of yogurt starter bacteria in single strain cultures. Food Bioprod Process (2014), http://dx.doi.org/10.1016/j.fbp.2014.09.007

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modified Arrhenius law describes the effect of temperature on the growth rate constant has been presented by Johnson et al. (1954) and Esener et al. (1981).

fT =

e−(Ea /RT)

(2)

1 + Ae−(Ga /RT)

2.2.

Function of pH (fpH )

Schepers et al. (2002b) applied the Gaussian equation for describing the influence of pH on the growth of L. helveticus. In the present work, a four parameter equation was presented to describe the effect of pH on the growth rate: 2

fpH =

C1 (pHopt − pH) + C2 2

(pHopt − pH) + C3

(3)

2.3. Function of carbon and nitrogen substrate (fSC and fSN )

fSC =

Csc Csc + Kc

(4)

fSN =

CSN CSN + KN

(5)

Function of lactate and lactic acid (fLa and fHla )

For describing the influence of product inhibition on lactic acid bacteria, some researchers have separated the effect of dissociated and undissociated forms of lactic acid on the growth rate by considering two terms (Venkatesh et al., 1993; Schepers et al., 2002b). Since total lactic acid concentration (P) is equal to the sum of its dissociated and undissociated forms (CP = CHLa + CLa ), these concentrations can be obtained according to the Henderson–Hasselbach correlation. CHla =

CLa =

CP

(6)

1 + 10(pH−pKa) CP

(7)

1 + 10(pKa−pH)

Lactic acid inhibitory effect has been described as an exponential function for L. helveticus by Schepers et al. (2002b) and as a linear function for L. bulgaricus by Gadgil and Venkatesh (1997). The inhibitory effect of lactic acid was better described by Eq. (8) (Schepers et al., 2002b) for experimental data obtained in this study. fHla =



1 1 + eKp (CHla −KHla )

 (8)

In previous studies, the effect of lactate on bacterial growth rate has been described as a linear function by Venkatesh et al. (1993) and an exponential function by Schepers et al. (2002b). The inhibitory effect of lactate was better described by this exponential function in this study. fLa = e−KLa .CLa

Lactic acid production rate

Luedeking–Piret equation was applied to describe the lactic acid production rate (rp ) (Luedeking and Piret, 2000) as follows: rp =

dX dCP = ai i + bi Xi dt dt

(9)

(10)

where a is the growth associated and b is the non-growth associated parameters.

2.6.

Substrates consumption rates

While carbon substrate is converted into biomass, lactic acid, and a trace amount of secondary metabolites, carbon substrate consumption rate is equal to the sum of product and biomass formation rates (Venkatesh et al., 1993). This rate equivalency was obtained by the following equation: dX dCP dCSC = −1.12 i − 0.95 dt dt dt

The Monod model was applied to describe the substrate limitation terms:

2.4.

2.5.

3

(11)

where the first term in the right hand side defines the conversion of substrate in to biomass and the second term defines the substrate conversion to lactic acid. The constants of Eq. (11) were taken from literatures (Venkatesh et al., 1993; Gadgil and Venkatesh, 1997). The usable nitrogen content in nitrogen source is converted into biomass. Thus, the nitrogen substrate consumption rate is given as: dCSN dX = −ın i dt dt

3.

Materials and methods

3.1.

Strains and media

(12)

S. thermophilus PTCC 1738 (ATCC 19258) was obtained from the microbial collection of the Iranian Research Organization for Science and Technology. L. delbrueckii ssp. bulgaricus was isolated from a traditional yogurt specimen. One mL of this yogurt was transferred to 10 mL MRS broth and cultivated at 45.0 ◦ C overnight. After that 0.1 mL of this broth transferred to a new MRS broth and repeated several times in order to omit Streptococcus’s. The final solution was appropriately diluted and propagated over a MRS agar plate under 5% CO2 pressure in the incubator. After several purification stages, a single colony was examined by applying colony and cell morphology, gram staining, catalase reaction and sugar fermentation pattern. The isolated bacterium was identified as a L. bulgaricus strain. The stock cultures were kept in deep-frozen stock at −80 ◦ C (Schepers et al., 2002a). Stock cultures were prepared from a pure culture at controlled pH and temperature; pH = 6.50, T = 40.0 ◦ C for S. thermophilus and pH = 5.70, T = 44.0◦ C for L. bulgaricus (Beal et al., 1989). They were harvested at the end of exponential growth, and stored with 50 g/L glycerol in microtubes and frozen at −80.0 ◦ C (Beal et al., 2001). Working cultures of L. bulgaricus were prepared from frozen stocks in MRS medium, inoculated at 1% (v/v) and incubated for 18 h at 42.0 ◦ C. Working cultures of S. thermophilus were prepared from frozen stocks in M17 medium, inoculated at 1% (v/v) and incubated for 18 h at 38.0 ◦ C. These cultures were propagated twice in the same conditions and used as inoculums to the bioreactor (Schepers et al., 2002a).

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Whey powder was obtained from Isfahan Pegah Dairy Company and dissolved in water to attain a 10% (w/v) concentration. The solution was autoclaved at 110 ◦ C for 20 min and filtered by filter paper to eliminate the coagulated proteins (Beal et al., 2001). Then, 800 mL of the filtrate and 1 mL Tween 80 (Merck) were sterilized in a 1 L in-house manufactured bioreactor. The bioreactor was equipped for continuous mixing, automatic pH and temperature recorder and controller, and an inert gas purge flow. Just before the fermentation process, 100 mL of sterile 10% (w/v) solution of yeast extract (Merck) was added to the bioreactor. In addition, 1 mL of each of the following sterile solutions, (1 M) MgSO4 and (1 M) CaCO3 (Merck) were added to the bioreactor, due to their positive effect on the growth of L. bulgaricus (Webb, 1948; Wright and Klaenhammer, 1983).

3.2.

Table 1 – Experimental conditions based on RSM for each bacterium.

1 2 3 4 5 6 7 8 9 10 11 12

L. bulgaricus

S. thermophilus

Tc

pHc

T (◦ C)

pH

T (◦ C)

−1 −1 1 1 −1.41 1.41 0 0 0 0 0 0

−1 1 −1 1 0 0 −1.41 1.41 0 0 0 0

40.0 40.0 48.0 48.0 38.3 49.6 44.0 44.0 44.0 44.0 44.0 44.0

4.90 6.50 4.90 6.50 5.70 5.70 4.56 6.83 5.70 5.70 5.70 5.70

36.0 36.0 44.0 44.0 34.3 45.6 40.0 40.0 40.0 40.0 40.0 40.0

pH 5.70 7.30 5.70 7.30 6.50 6.50 5.36 7.63 6.50 6.50 6.50 6.50

Analysis a

The samples were taken at 30 min intervals and placed in the refrigerator (Beal et al., 1989). The microbial growth was measured by microscopy using Eeverfocus YJ-2001 T light microscope and a Z30000 Helber Counting Chamber, i.e. a hemocytometer with 0.02 mm depth made by Howksley Company for bacterial cell enumeration. 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. Initial concentration of lactose in whey solution as determined by colorimetric dinitrosalicylic acid (DNS) method (Miller, 1959) was about 60 g/L. Lactic acid concentration was determined by the intermittent addition of 5 N NaOH to the bioreactor at appropriate time intervals using a peristaltic pump (Beal and Corrieu, 1995). Also, the NaOH solution was used to neutralize produced lactic acid to control pH in the vicinity of set point. The automatic recording and control of fermentation was performed by developed software. Amount of produced lactic acid and its production rate were calculated and recorded by the software knowing the amount of consumed NaOH. Amount of consumed lactose was calculated using a correlation derived from empirical equations by Beal and Corrieu (1995): CSC = [CSC0 /342 + (m/90) × CP ] × 342

(13)

where m was considered equal to −0.54 and −0.61 for S. thermophilus and L. bulgaricus, respectively, and CSC0 was the initial concentration of lactose (Beal and Corrieu, 1995). The yield of biomass on nitrogen substrate (YSNx ) for S. crernoris and L. helveticus is about 1.0 (g biomass/g nitrogen) (Nielsen et al., 1991; Schepers et al., 2002b). The same value was assumed in this study for this parameter. Thus, the nitrogen substrate concentration throughout the fermentation can be calculated by the following linear equation: CSN = CSN0 − (1/YSNx )Xi

(14)

where CSN0 is the initial concentration of yeast extract.

3.3.

Coded valuesa

Run

Coded value of a variable x is defined as: xc = 2(x − x0 )/(x+1 − x−1 ) in which x−1 and x+1 are high and low factorial points selected for the variable. x0 is center point value i.e. x0 = (x−1 + x+1 )/2.

for each bacterium was conducted in batches with different pH and temperatures according to Table 1. The parameters of the Luedeking–Piret equation were estimated for each experiment by applying the non-linear curve fitting function (lsqcurvefit) in Matlab 7.12.0. (R2011a, The MathWorks Inc., Natick, MA, USA). Analysis of variance was performed for maximum cell population, maximum specific growth rate and total produced lactic acid, growth associated and non-growth associated parameters of Luedeking–Piret equation. Optimum pH and temperature for the growth of these bacteria were estimated by RSM analysis. Design of experiments and statistical analysis were performed using SAS software (version 9.0; SAS Institute Inc., Cary, NC, USA).

3.4.

Parameter estimation and model prediction

Biomass, lactic acid, nitrogen, and carbon substrate concentrations from each set of experiments were the input data for SBToolbox2 on Matlab. The combination of Eqs. (1), (10), (11) and (12) along with Eqs. (2)–(9) constituted the basis of the developed model. Parameters of the model were estimated by applying particle swarm algorithm provided by SBToolbox2 with its default options (Vaz and Vicente, 2007, 2009; Henkel et al., 2011). The particle swarm algorithm minimizes the sum of quadratic differences between measurements and simulations, and reports the minimum function which shows the best goodness of fitting (Henkel et al., 2011). The closer the minimum function is to zero the better the fitting. In the present study, the possible range of parameters was controlled by upper and lower bounds, and initial guess, adjusted according to the studies by Venkatesh et al. (1993) and Schepers et al. (2002b). Referring to Eqs. (1)–(12), the governing set of equations of the proposed model is:

⎡

Experimental design

Central Composite, Uniform Precisions design of RSM was applied with 12 runs in order to estimate the effect of pH and temperature on the growth and acid production of each bacterium. This design included 4 factorials, 4 axials, and 4 center points that were considered for each bacterium with different pH and temperature levels (Table 1). Every set of experiments

⎡

1

⎢ 1.19 ⎢ i ⎣ −a

0

0

1 0.95 0

1

1.08 0

0

⎤⎢ ⎢ ⎢ 0⎥⎢ ⎥⎢ 0⎦⎢ ⎢ 1 ⎢ ⎣ 0

i dXm dt

dCSC dt dCP dt dCSN dt

⎤ ⎥ ⎡  f f f f f f Xi ⎤ ⎥ max T pH La HLa SN Sc m ⎥ i ⎥ ⎢ ⎥ b i Xm ⎥=⎢ ⎥ (15) ⎥ ⎣ ⎦ 0 ⎥ ⎥ 0 ⎦

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To simulate the bacterial growth and lactic acid production, the ode23 function of Matlab was applied based on the Trapezoidal rule. Coefficient of determination, i.e. R2 , and Root Mean Square Error (RMSE) between predicted and experimental points for each experiment was calculated to evaluate the goodness of fitting.

4.

Results and discussion

4.1.

Statistical analysis of RSM

RSM analyses of S. thermophilus and L. bulgaricus single strain cultures showed that pH and temperature had a significant effect on the growth of these bacteria at the examined range. Specifically, the effect of pH2 on the growth and acid production of S. thermophilus and L. bulgaricus was highly significant. Optimum pH and temperature were obtained to be 7.00 and 42.8 ◦ C for the growth of S. thermophilus, and 5.20 and 44.0 ◦ C for the growth of L. bulgaricus. The optimum temperature was in agreement with the results of Beal et al. (1989); however, they reported optimum pH to be 5.8 and 6.5 for L. bulgaricus and S. thermophilus, respectively. The differences between the two sets of optimum pH values may be due to the differences in strains or medium compositions used in these two works. Medium composition used in the mentioned work was a mixture of mild whey, lactose, yeast extract and peptone. Different buffering capacity resulted from different medium composition might influence pH tolerance of the bacteria (Parente and Zottola, 1991). According to analysis of variance, pH and temperature had not significant effect on the parameters of Luedeking–Piret equation. Thus, in the developed model these parameters were assumed to be constant. The growth associated parameter for L. helveticus was also independent of pH and temperature; however, the non-growth associated parameter was pH-dependent (Schepers et al., 2002b). The growthassociated parameter for L. bulgaricus reported by Venkatesh et al. (1993) is greater than the value obtained in this study.

4.2.

Estimated parameters

The parameters of pH, temperature, carbon and nitrogen substrate, and dissociated and undissociated lactic acid functions from Eq. (1) and parameters of the Luedeking–Piret equation were estimated for each set of experiments with L. bulgaricus and S. thermophilus (Table 2). The minimum function reported by SBToolbox2 for the twelve experiments of L. bulgaricus was about 0.012 and of

Table 2 – The estimated parameters of the model for L. bulgaricus and S. thermophilus. Parameter

S. thermophilus

L. bulgaricus

max A Ea Ga pHopt C1 C2 C3 Kc KN Kp KHla KLa a

1.18 1.2E+6 130 52,160 6.87 45.42 11.25 0.123 1.0E−6 253.1 52.862 0.0444 0.3259 1.54

1.95 1.9E+6 80 55,430 5.25 6.64 69.32 2.769 2.485 124.7 0.498 1.0E−5 0.4400 0.70

b

0.52

0.60

ın

0.98

1.08

Unit 1/h – kJ/gmol kJ/gmol – – – – g/L g/L L/g g/L L/g g lactic acid/g biomass g lactic acid/(g biomass h) g biomass/g nitrogen

S. thermophilus was about 0.023. The minimum function is a measure of fitting error and so these small quantities represents high goodness of fit resulted from the values depicted in Table 2.

4.3.

Function of temperature (fT )

In previous studies, the effect of temperature on the specific growth rate has been investigated as the only parameter that affects the growth rate (Esener et al., 1981; Ratkowsky et al., 1982; Ratkowsky et al., 1983). According to the knowledge of the authors, no study has considered the effect of temperature in the kinetic model as it is mentioned here. Compared with the second order model of (Ratkowsky et al., 1982; Ratkowsky et al., 1983), Eq. (2) described better the effect of temperature. As it can be seen in Fig. 1, function of temperature for both bacteria which presented a bell-shaped curve, as it was reported in literatures (Johnsen et al., 1954; Esener et al., 1981). Optimum temperature was about 42 ◦ C for S. thermophilus and about 45 ◦ C for L. bulgaricus which was in agreement with result of RSM (Fig. 1). Ga was similar for both microorganisms as it expresses the thermal enzyme inactivation energy of the bacteria (Villadsen et al., 2011; Esener et al., 1981). Ea for both bacteria was in agreement with the results of Villadsen et al. (2011) and Esener et al. (1981). Variation of fT with temperature was somehow slight in the examined range which was not expected for these two bacteria. However, this function

Fig. 1 – Plot of function of temperature vs. temperature for S. thermophilus (left) and L. bulgaricus (right). Please cite this article in press as: Aghababaie, M., et al., Developing a detailed kinetic model for the production of yogurt starter bacteria in single strain cultures. Food Bioprod Process (2014), http://dx.doi.org/10.1016/j.fbp.2014.09.007

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Fig. 2 – Plot of function of pH vs. pH for L. bulgaricus (left) and S. thermophilus (right). with the estimated parameters gave the best results for the presented model.

4.4.

and Corrieu, 1998; Rajagopal and Sandine, 1990; Tamime and Robinson, 2007). It is well known that L. bulgaricus is responsible for the sourness of yogurt by lowering its pH to below 4.

Function of pH (fpH )

The comparison of Eq. (3) with the Gaussian equation (Schepers et al., 2002b) revealed that the latter was not appropriate for the analysis of the experimental data of this study. As shown in Fig. 2, the values of the pH function of S. thermophilus was higher than that of the L. bulgaricus, which displayed the greater effect of pH on S. thermophilus growth. This function for L. bulgaricus had a dull curvature around optimum pH, while the same had a sharp curvature for S. thermophilus. These results revealed that S. thermophilus was more sensitive than L. bulgaricus with respect to pH. These results corresponded to RSM results with respect to the effect of pH. Many references indicate that L. bulgaricus tolerates lower pH, for example all reported optimum pH values for different L. bulgaricus strains are below 6 (Beal et al., 1989; Beal

4.5. Functions of carbon and nitrogen substrate (fC and fN ) In these experiments with initial lactose concentration of 60 g/L, carbon substrate was not a limiting factor due to the low value of Monod constants for carbon source (KC ) in comparison with the concentration of lactose in whey solution. This is in agreement with values reported by Burgos-Rubio et al. (2000) and Gadgil and Venkatesh (1997). It is well known that lactic acid bacteria are highly dependent to various growth factors such as amino acids and vitamins. Since yeast extract is the main source of these compounds in culture medium, growth rate of these bacteria depends on both quantity and quality of yeast extract which in many cases acts as growth limiting factor. Since nitrogen

Fig. 3 – Plot of lactic acid and lactate function vs. time for L. bulgaricus (a) pH = 4.56 and T = 44.0 ◦ C and (b) pH = 6.83 and T = 44.0 ◦ C (right). Please cite this article in press as: Aghababaie, M., et al., Developing a detailed kinetic model for the production of yogurt starter bacteria in single strain cultures. Food Bioprod Process (2014), http://dx.doi.org/10.1016/j.fbp.2014.09.007

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Fig. 4 – Plot of lactic acid and lactate function vs. time for S. thermophilus (a) pH = 5.36 and T = 40.0 ◦ C and (b) pH = 7.63 and T = 40.0 ◦ C (right).

limitation is usually observed instead of carbon limitation, it was expected to have larger values for Monod constant for nitrogen substrate (Bouguettoucha et al., 2011). Thus, high value of Monod constant for nitrogen substrate (KN ) revealed that yeast extract, the main usable nitrogen source, could be a limiting substrate.

4.6.

Functions of lactate and lactic acid (fLa and fHla )

Since concentrations of dissociated and undissocated forms of lactic acid vary with pH in each experiment, the inhibitory effect of lactate and lactic acid depends on the pH of the fermentation. The effect of these constituents on growth can be visualized by drawing their functions against fermentation time. This is performed for L. bulgaricus at two pH located at two sides of optimum pH (Fig. 3). At both plots, fLa began from 1.0 and gradually decreased by the production of lactic acid during the fermentation. The extent variations were somehow different for the two pH values. At pH = 6.83, the lactic acid is almost completely dissociated; therefore, undissociated lactic acid concentration was very low. Thus, fHla stayed constant, which revealed that this form of lactic acid has very little effect on the growth rate. At pH = 4.56, ratio of undissociated lactic acid to lactate ion is increased and hence its inhibitory effect becomes more considerable (Fig. 3). These reductions in lactate and lactic acid functions illustrated the inhibitory effect of the dissociated and undissociated forms of lactic acid during the fermentation. Similar plots were drawn at pH = 5.36 and pH = 7.36 for S. Thermophilus (Fig. 4). While the concentration of undissociated lactic acid was very low at pH = 7.63, the function of lactic acid was almost constant. At pH = 5.36, the inhibitory effect of undissociated lactic acid is obvious in Fig. 4. In contrast, fLa

generally decreased as lactic acid produced, which indicated the high inhibitory effect of lactate on S. thermophilus growth at both pH values. It is now recognized that inhibition by weak organic acids is related to the solubility of the undissociated form within the cytoplasmic membrane and the insolubility of the ionized acid (Bouguettoucha et al., 2011). Investigation of lactic acid inhibition effect on growth of L. rhamnosus has shown that for high pH values the intracellular ionic lactic acid concentration is the inhibitory species, whereas, for low pH values, the undissociated form of lactic acid plays that role (Gonc¸alves et al., 1997). Briefly, the result of the present study confirmed the inhibitory effect of undissociated form of lactic acid at low pH values and the inhibitory effect of dissociated form of lactic acid at higher pH values.

4.7.

Simulation of the experiments

Every set of 12 experiments for each bacterium was simulated with the kinetic model (Eq. (18)) by applying the parameter values presented in this study. Fig. 5 shows model predictions and experimental data of L. bulgaricus at different pH and temperature. According to Fig. 5, the model was able to cover data regarding growth and lactic acid production of S. thermophilus. This fact is verified by respective values of R2 and RMSE which are given in the figure caption. In Fig. 5b and c, a very good agreement between the experimental data and predicted model was observed for lactic acid production at different temperatures. Fig. 6 shows the good agreement between the experimental data and predicted model due to the presented R2 and RMSE values. According to Fig. 6a and b, the growth of

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Fig. 5 – Experimental data (symbols) and model prediction (lines) – biomass and lactic acid vs. time for L. bugaricus at various conditions (a) T = 44.0 ◦ C and pH = 4.56; R2 = 0.9577 and RMSD = 0.0052. (b) T = 44.0 ◦ C and pH = 6.83; R2 = 0.9913 and RMSD = 0.0007. (c) T = 38.3 ◦ C and pH = 5.70; R2 = 0.9995 and RMSD = 0.0409. (d) T = 40.0 ◦ C and pH = 6.50; R2 = 0.9117 and RMSD = 0.0652. S. thermophilus was well predicted in different pH values. As can be seen in Fig. 6c and d, the effect of temperature on lactic acid production was higher than that on the growth rate.

Goodness of fit for the presented model on experimental data is comparable with the results of other reported attempts for mathematical modeling of lactic acid bacteria cultivation (Ishizaki et al. 1989; Venkatesh et al., 1993; Gadgil and

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Fig. 6 – Experimental data (symbols) and model prediction (lines) for biomass and lactic acid vs. time for S. thermophilus at various conditions (a) T = 36.0 ◦ C and pH = 5.70; R2 = 0.9237 and RMSD = 0.0055. (b) T = 36.0 ◦ C and pH = 7.30; R2 = 0.9984 and RMSD = 0.0163. (c) T = 45.6 ◦ C and pH = 6.50; R2 = 0.8661 and RMSD = 0.0418. (d) T = 40.0 ◦ C and pH = 6.50; R2 = 0.9998 and RMSD = 0.0074. Venkatesh, 1997; Åkerberg et al., 1998; Luedeking and Piret, 2000; Burgos-Rubio et al., 2000; Alvarez et al., 2010). However, in these works, the parameres of the models have been estimated separately by fitting the model to the experimantal

data of each batch or by estimating the effct of each factor on the pre-determined spesific growth rate. On the contrary, the presented model is fitted simultanously to all of the eaperimnatal data of 12 batches which was run for each bacterium.

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Thus, it was expected to have larger error in simulating several batches with one set of parameters than that with using one separate set for each batch. The mentioned method of fitting was inevitable since pH and temperture was constant in each experiment, though changed from one experiment to another one. In spite of this, this model was able to predicte a growth and acid production of these baceria in single strain culture, properly.

5.

Conclusion

In this work a kinetic model predicted the growth and lactic acid production of L. bulgaricus and S. thermophilus in single strain pH-controlled batch cultures as a function of pH, temperature, carbon substrate, nitrogen substrate, biomass, and lactic acid concentration. The RSM results confirmed that the growth conditions of S. thermophilus and L. bulgaricus were pH and temperature dependent in the investigated ranges; however, parameters of Luedeking–Piret equation were independent of pH and temperature. The obtained results confirmed that this model is capable of predicting the bacterial growth at different pH and temperatures in the range of 5.36 to 7.63 and 34.3 ◦ C to 45.6 ◦ C for S. thermophilus and in the range of 4.56–6.83 and 38.3–49.6 ◦ C for L. bulgaricus. This model is useful for simulating and controlling the single strain fermentation process of these bacteria. According to the estimated parameters of the function of pH, the optimum pH for L. bulgaricus and S. thermophilus were about 5.25 and 6.88, respectively, which was in good agreement with the results of RSM. The inhibitory effect of lactic acid and lactate ion was evident in this model, while undissociated form of lactic acid was the main inhibitory form at low pH values and dissociated form of lactic acid was the main inhibitory form at higher pH values. This newly introduced model can be applied for simulating and controlling the single strain fermentation of S. thermophilus and L. bulgaricus. Furthermore, this model can pave the way for future studies in developing a kinetic model for mixed cultures of these two bacteria. The proposed kinetic model might be applicable for other species of lactic acid bacteria growing on various substrates and different ranges of pH and temperature. However, with different set of parameter values which should be obtained via fitting of the model to respective experimental data.

Acknowledgments This study was financially supported by the Isfahan Center for Research on Agricultural Science and Natural Resources, and the University of Isfahan.

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