NEW APPROACH TO MODELLING THE KINETICS OF THE FERMENTATION PROCESS IN CULTIVATION OF ... ·...

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NEW APPROACH TO MODELLING THE KINETICS OF THE FERMENTATION PROCESS IN CULTIVATION OF LACTIC ACID BACTERIA Georgi Kostov*, Rositsa Denkova-Kostova**, Vesela Shopska*, Petar Nedyalkov*, Zapryana Denkova*** *Department of Wine and Beer ** Department of Biochemistry and Molecular Biology”; *** Department of Microbiology University of Food Technologies, 4002, 26 Maritza Blvd., Plovdiv, Bulgaria E-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected] Bogdan Goranov LBLact, Plovdiv, Bulgaria, E-mail: [email protected] Vasil Iliev Weissbiotech, Ascheberg, Germany, E-mail: [email protected] Kristina Ivanova, Desislava Teneva Food Research and Development Institute, Е-mail: [email protected]; [email protected] KEYWORDS Lactic acid bacteria, kinetic, modelling, semi-empirical models ABSTRACT The present paper reviews the methods for assessing the kinetics of the fermentation process for the cultivation of probiotic strains of lactic acid bacteria in a laboratory bioreactor with stirring. To describe the kinetics of the lactic acid fermentation process, an alternative approach with the use of semi-empirical degree laws that offer a new look into the biological parameters in the description models is proposed. INTRODUCTION Probiotic lactic acid bacteria Lactobacilli belong to the natural microflora of human and animal organisms. They normally exist in the oral cavity, gastrointestinal tract, and vaginal microflora (Adams, 1999). The most common lactobacilli species isolated from the gastrointestinal tract of humans are Lactobacillus brevis, Lactobacillus casei, Lactobacillus acidophilus, Lactobacillus plantarum, Lactobacillus fermentum and Lactobacillus salivarius (Slover, 2008). The cellular components of certain lactic acid bacteria protect and modulate the immune system of the human body and improve its health status (Pirt, 1975; Salminen and von Wright, 1998a,b). L. delbrueckii ssp. bulgaricus, L. acidophilus, L. casei, L. plantarum are the major microorganisms that regulate the balance of the gastrointestinal microflora (Salminen and Wright, 1998b). Lactic acid bacteria provide the human organism with growth factors, amino acids, vitamins, organic acids, etc. through their metabolism. They have the ability to adhere to the intestinal mucosa, stop the formation of enterobacterial colonies, and prevent the colonization of the gut epithelium by bacteria coming from outside (Pirt, 1975). These regulatory functions are realized by the organic acids, bacteriocins, bacteriocin- like substances (BLIS), and other metabolites produced by lactic acid bacteria through which they inhibit enteropathogens (Fang, 2001). Lactic acid bacteria and their metabolic products have beneficial effects on the digestive system and positive action during and after antibiotic treatment (O'Brien et al., 1999). The mechanism of action of lactobacilli comprises: a) suppression of microbial putrefaction processes; b) prevention of constipation, colon cancer, etc.; c) prevention and treatment of antibiotic-associated diarrhea; d) stimulation of the immune system; e) suppression of toxic processes in the digestive tract (Pirt, 1975; Fuller, 1986; Salminen and Wright, 1998a,b). Lactic acid bacteria are also characterized by antimutagenic, anticancerogenic and antitumor activity (Hosono et al., 1990). Lactic acid bacteria with proven probiotic properties are included in the composition of probiotic preparations, starter cultures, and in the production of dairy, meat and other products with functional properties. One of the requirements for a strain to be probiotic is that it would allow industrial processes to take place, including cultivation, and accumulation of high concentrations of viable probiotic cells in the cultivation process. One of the main stages in the production of probiotics and starter cultures is the cultivation of the selected strains in industrial bioreactors of different construction. The cultivation process defines mainly the qualitative and quantitative characteristics of the production process as a whole. Methods of cultivation A. Batch cultivation. In this method, the microbial population grows in a closed space without changing the medium volume; without the addition of any substrates, and with the addition of substances that correct some of the parameters only. Process parameters are a function of time, and the process is non-stationary. Batch cultivation of lactic acid bacteria is characterized by the following stages (Abdel-Rahmanq et al., 2013): • Lag-phase: it occurs immediately after inoculation of the nutrient medium and aims at adapting the microbial population to the conditions of the medium. Cells undergo biochemical processes of synthesis of cellular structures needed for the binary fission. Additionally, if Proceedings 32nd European Conference on Modelling and Simulation ©ECMS Lars Nolle, Alexandra Burger, Christoph Tholen, Jens Werner, Jens Wellhausen (Editors) ISBN: 978-0-9932440-6-3/ ISBN: 978-0-9932440-7-0 (CD)

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NEW APPROACH TO MODELLING THE KINETICS OF THEFERMENTATION PROCESS IN CULTIVATION OF LACTIC ACID

BACTERIAGeorgi Kostov*, Rositsa Denkova-Kostova**, Vesela Shopska*, Petar Nedyalkov*, Zapryana Denkova***

*Department of Wine and Beer ** Department of Biochemistry and Molecular Biology”; *** Department of MicrobiologyUniversity of Food Technologies, 4002, 26 Maritza Blvd., Plovdiv, Bulgaria

E-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected] Goranov

LBLact, Plovdiv, Bulgaria, E-mail: [email protected] Iliev

Weissbiotech, Ascheberg, Germany, E-mail: [email protected] Ivanova, Desislava Teneva

Food Research and Development Institute, Е-mail: [email protected]; [email protected]

KEYWORDS

Lactic acid bacteria, kinetic, modelling, semi-empiricalmodels

ABSTRACTThe present paper reviews the methods for assessing thekinetics of the fermentation process for the cultivation ofprobiotic strains of lactic acid bacteria in a laboratorybioreactor with stirring. To describe the kinetics of thelactic acid fermentation process, an alternative approachwith the use of semi-empirical degree laws that offer anew look into the biological parameters in the descriptionmodels is proposed.

INTRODUCTIONProbiotic lactic acid bacteriaLactobacilli belong to the natural microflora of humanand animal organisms. They normally exist in the oralcavity, gastrointestinal tract, and vaginal microflora(Adams, 1999).The most common lactobacilli species isolated from thegastrointestinal tract of humans are Lactobacillus brevis,Lactobacillus casei, Lactobacillus acidophilus,Lactobacillus plantarum, Lactobacillus fermentum andLactobacillus salivarius (Slover, 2008).The cellular components of certain lactic acid bacteriaprotect and modulate the immune system of the humanbody and improve its health status (Pirt, 1975; Salminenand von Wright, 1998a,b). L. delbrueckii ssp. bulgaricus,L. acidophilus, L. casei, L. plantarum are the majormicroorganisms that regulate the balance of thegastrointestinal microflora (Salminen and Wright,1998b). Lactic acid bacteria provide the human organismwith growth factors, amino acids, vitamins, organicacids, etc. through their metabolism. They have theability to adhere to the intestinal mucosa, stop theformation of enterobacterial colonies, and prevent thecolonization of the gut epithelium by bacteria comingfrom outside (Pirt, 1975). These regulatory functions arerealized by the organic acids, bacteriocins, bacteriocin-like substances (BLIS), and other metabolites producedby lactic acid bacteria through which they inhibitenteropathogens (Fang, 2001).

Lactic acid bacteria and their metabolic products havebeneficial effects on the digestive system and positiveaction during and after antibiotic treatment (O'Brien etal., 1999).The mechanism of action of lactobacilli comprises: a)suppression of microbial putrefaction processes; b)prevention of constipation, colon cancer, etc.; c)prevention and treatment of antibiotic-associateddiarrhea; d) stimulation of the immune system; e)suppression of toxic processes in the digestive tract (Pirt,1975; Fuller, 1986; Salminen and Wright, 1998a,b).Lactic acid bacteria are also characterized byantimutagenic, anticancerogenic and antitumor activity(Hosono et al., 1990).Lactic acid bacteria with proven probiotic properties areincluded in the composition of probiotic preparations,starter cultures, and in the production of dairy, meat andother products with functional properties. One of therequirements for a strain to be probiotic is that it wouldallow industrial processes to take place, includingcultivation, and accumulation of high concentrations ofviable probiotic cells in the cultivation process. One ofthe main stages in the production of probiotics and startercultures is the cultivation of the selected strains inindustrial bioreactors of different construction. Thecultivation process defines mainly the qualitative andquantitative characteristics of the production process as awhole.Methods of cultivationA. Batch cultivation. In this method, the microbialpopulation grows in a closed space without changing themedium volume; without the addition of any substrates,and with the addition of substances that correct some ofthe parameters only. Process parameters are a function oftime, and the process is non-stationary. Batch cultivationof lactic acid bacteria is characterized by the followingstages (Abdel-Rahmanq et al., 2013):• Lag-phase: it occurs immediately after inoculation ofthe nutrient medium and aims at adapting the microbialpopulation to the conditions of the medium. Cellsundergo biochemical processes of synthesis of cellularstructures needed for the binary fission. Additionally, if

Proceedings 32nd European Conference on Modelling and Simulation ©ECMS Lars Nolle, Alexandra Burger, Christoph Tholen, Jens Werner, Jens Wellhausen (Editors) ISBN: 978-0-9932440-6-3/ ISBN: 978-0-9932440-7-0 (CD)

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the medium contains high molecular weight molecules,the cells release extracellular enzymes to break themdown to low molecular weight compounds, therebyfacilitating their intracellular transport.• Exponential phase: the cells grow and divideintensively. They multiply at a maximum rate.• Stationary phase: there is depletion of one or moresubstances from the growth medium, and the cells stopmultiplying. During the stationary phase, the number ofnewly formed cells is equal to the number of dying cells,so no increase in biomass is observed, but the cells havea preserved metabolic activity.• Death phase: during this phase, the number of cells thatare dying is significantly greater than the number ofnewly formed cells.B. Batch cultivation with pH correction.The constantly increasing concentration of lactic acidduring batch cultivation has an inhibitory effect on thegrowth of lactic acid bacteria. To remove it, pHadjustment is required during the batch fermentationprocess. The correction is accomplished by the additionof NaOH, KOH, CaCO3, and ammonia water, and leadsto a fuller absorption of the substrate and an increase inthe amount of lactic acid produced and accumulated(Hetenyi et al., 2011, Abdel-Rahman et al., 2011a, b,Adsul et al., 2007; Tashiro et al., 2011). According to anumber of authors, the optimum pH range for the growthof lactic acid bacteria is between 5 and 6 (Fu andMathews 1999, Yuwono and Kokugan 2008).C. Continuous fermentation.Continuous cultivation systems provide increasedproductivity and reduce the inhibitory effect of lactic acidon cell growth. They are classified as open and closedcontinuous cultivation systems.The most important factors for the production ofprobiotic products in continuous mode are the closedcontinuous cultivation systems. The targetedmanagement of the lactic acid fermentation process is animportant indicator for ensuring the quality of lactic acidfoods and liquid probiotic preparations. The main pointin the technological process is the provision of optimalconditions for the growth of the microbial cells, ensuringthe accumulation of high active flora concentration, andcreating conditions for obtaining standardized starterswith constant properties and biochemical activity(Driessen et al., 1977).Kinetic models for lactic acid fermentationdescription.The description of the kinetics of microbial growth isdone through a number of models. Currently, differenttypes of dependencies are used in practice, many ofwhich are based on Monod's classic equation, but thereare other types of models that offer a new look at thefermentation process.The Monod equation expressing the specific growth ratedependence on the concentration of the limiting substrateis analogous to the Michaelis-Menten equation(Bouguettoucha, et al., 2011; Abboud et al., 2010; Deyand Pal, 2013; Ghaly et al., 2005):

max S

Sµ µK S

(1)

where: μ - specific growth rate, h-1; μmax - maximumspecific growth rate, h-1; Ks - saturation constant,kg/m3; S - substrate concentration kg/m3. Thesaturation constant is equal to the substrateconcentration at which the specific growth rate is halfof its maximum value (μ = 0.5μmax).

High concentrations of the substrate can lead to cellgrowth inhibition. This process should be taken intoaccount when developing the mathematical model. TheAndrews-Halden model is one of the most commonlyused models for description of the inhibitory action ofhigh substrate concentrations (Abboud et al., 2010, Deyand Pal, 2013; Bouguettoucha et al., 2011).

max 2 S

i

Sµ µSK SK

(2)

where: Ki - inhibition constantAnother model for describing the inhibitory action ofhigh substrate concentrations is the Edward model(Abboud et al., 2010; Dey and Pal, 2013; Bouguettouchaet al., 2011):

max 2 ( ) (1 )S

i

Sµ µSK SK

(3)

The specific growth rate depends not only on theconcentration of the limiting substrate but also on otherfactors, primarily the concentration of the metabolicproducts. Yerusalimski proves that this dependence isdescribed by the non-competitive inhibition equation(Abboud et al., 2010; Dey and Pal, 2013; Bouguettouchaet al., 2011):

max P

P

Kµ µK P

(4)

where: P - concentration of the inhibitory product,kg/m3; Kp - constant, kg/m3.Kp is the concentration of the inhibitory product inwhich the specific growth rate is equal to half of itsmaximum value (μ=0.5μmax).

All growth parameters in the previous models have noclear biological meaning. The biological requirement ofthe model parameters is satisfied by the Verhulstequation (Bouguettoucha et al., 2011):

2 2

K

dX X X X Xd X

(5)

where: X – biomass concentration, kg/m3; Xk – finalbiomass concentration, kg/m3; β - coefficient ofinternal population competition, kg/(kg.h)

SEMI-EMPIRICAL MODELS: A NEWAPPROACH TO THE DESCRIPTION OFMICROBIAL KINETICSDifferential equations used in practice for describing thelactic acid process are rarely solved with high accuracy,largely due to the presence of too many ambiguousvariables. This is particularly true of the more complexmodels describing the kinetics of the fermentation

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process. Thus, a purely numerical solution can hardly befound, and in some cases the solution to a task is semi-empirical rather than analytical (Tishin and Fedorov,2016).In their works, Tishin and Fedorov, 2016; Tishin et al.,2015 suggest the use of a different principle fordescribing microbial kinetics. It is based on variousassumptions about continuous cell division and theproportionality of biomass accumulation in time, itsconcentration in the culture medium and the cultivationtime. In this case, cell multiplication can be describedwith the following dependence:

m ndX kX (6)where: k - a proportionality factor, m and n - degreeindicators.

Depending on the values of the degree indicators,different mathematical models can be obtained for thesame fermentation process.For example, at n = 0 the step model (7) is obtained, andthe coefficient k1 is analogous to the specific growth rateμ (Tishin and Fedorov, 2016).

1mdX k X (7)

In real form, after integration, equation (7) acquires theform:

110

(1 ) 11mB m

m kXX

(8)

Equation (8) can be converted by entering parameter δand assuming that:

11

1m

m

(9)

where: 11 m

BX (10)According to Tishin et al., 2015, parameter δ is theaverage specific growth rate for the entire cultivationprocess interval.In the second case, the differential equation can be solvedif m = 0 and n = 1 are known:

2ndX k X (11)

After integrating the obtained equation and dividing byx0:

1 12

1 0

1( 1)

nB

kXn X

(12)

If the parameter γ, which is the ratio on the right side ofequation (12), is introduced, the following is obtained:

1 nBX (13)

γ can be considered an average specific growth rate, butit has a much clearer meaning since it can easily be shownthat 1/γ represents the doubling time of the cellpopulation (Tishin and Fedorov, 2016 Tishin et al.,2015).Using Equations (8) and (13), equations for the substrateconsumption during the fermentation process can also bederived. The detailed solution is presented in Tishin andFedorov, 2016; Tishin et al., 2015, where dependenciesof the following type are obtained:

1

1(1 ) sm

s

S

(14)

1(1 ) sn

s

S

(15)

Tishin and Fedorov, 2016; Tishin et al., 2015 show thatequations (13) and (15) have a clearer biological sense oftheir parameters and are therefore preferable whendescribing the kinetics of the fermentation process.On the basis of equations (6) to (15), other types ofprocess equations are also proposed, which also includethe knowledge of kinetics when using the classicalequations (1) to (5) (Tishin and Fedorov, 2016): exponential degree model

( )BX a d e (16) modified empirical model of the logistic curve

11B mX

be

(17)

Weibull's equation for describing lactic acidbiosynthesis

( )qT m eK c c

(18)where XB - biomass in a dimensionless form; μ - specificrelative (average) growth rate of biomass at a timeinterval from τ = 0 to τ = τi; μm - maximum specificgrowth rate, h-1; a, b and d - empirical coefficientscarrying certain biological meaning; cm - maximum valueof titratable acidity, °T; c - coefficient equal to thedifference between the maximum and the initial titratableacidity, °T; q - specific rate of acid formation,°T/cfu.cm3.h; δ - an indicator defining the change in thecurve shape or the change in the rate of lactic acidaccumulation over time; τ- time of cultivation, h.The advantage of this type of model lies in the fact that itcan easily be solved by simple methods and does notrequire complicated numerical solution programs, butalso allows for a different kind of interpretation of thebiological processes observed in the cultivation ofmicroorganisms.The aim of the present work was to apply these types ofmodels to describe the process of cultivation of probioticlactic acid bacteria under static and dynamic (cultivationin a bioreactor) conditions, and to present the possibilitiesfor interpreting the obtained results and the biologicalmeaning of the variables.

MATERIALS AND METHODS

MicroorganismsThe study was conducted with two strains of differentlactobacilli species: Lactobacillus delbrueckii ssp.bulgaricus TAB2 isolated from spontaneously fermenteddairy products, and Lactobacillus plantarum BZ3isolated from spontaneously fermented vegetables.Nutrient media (ISO 7889:2005)• MRS - broth;• MRS-agar;• Saline solution.Methods of analysis• Determination of titratable acidity (ISO/TS11869:2012);

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• Number of viable lactobacilli cells (ISO 7889:2005).Batch cultivation• Under static conditions. Cultivation was carried out inflasks thermostated at 37±1°C;• Cultivation in a bioreactor. Cultivation was carried outin the laboratory bioreactor shown in Fig. 1. Theapparatus has a geometric volume of 2 dm3 and a workingvolume of 1.5 dm3 and is equipped with a Sartorius A2control device, which includes all the measuringinstruments for the fermentation process: temperature,pH, dissolved oxygen, etc. The fermentation process wascarried out at a stirring speed of 150 rpm at 37±1°C.

Figure 1: Laboratory bioreactor1 - vessel with a geometric volume of 2 dm3; 2 - baffles; 3 -temperature electrode (thermometer); 4 - cooling/heatingdevice (water jacket); 5 - an additional cooling/heatingdevice; 6 - turbine stirrer; 7 - pH/Eh electrode; 8 -fermentation medium/inoculum/pH adjustment medium; 9 -peristaltic pump; 10 - stirrer drive; 11 – Sartorius A2 controldevice;

Models for describing the kinetics of the fermentationprocessThe description of the kinetics was made using equations(16) to (18). The process parameters were defined usingTableCurve2D and Excel. The software was also used forconducting statistical evaluation of the obtained models.

RESULTS AND DISCUSSION

The results of the studies on the dynamics of thefermentation process under static and dynamic conditionsare presented in Fig. 2 and Fig. 3, and in Table 1 andTable 2. Biomass data are displayed in dimentionlessform relative to the initial cellular concentrationimmediately after inoculation of the medium.In the cultivation of L.delbrueckii ssp. bulgaricus TAB2,shortening of the lag-phase from 6 to 3 hours duringdynamic cultivation was observed. At the same time,cultivation in a bioreactor led to the accumulation of oneorder higher concentration of viable lactobacilli cells, andas a result, about 1012 cfu/cm3 were accumulated in theapparatus compared to static cultivation (Fig. 2.). Thetitratable acidity values were close and were in the rangebetween 170-190°T (Fig. 2). The data on the static anddynamic cultivation of L. planarum BZ3 were similar(Fig. 3). About 1013cfu/cm3 of L. plantarum cells weregrown in the bioreactor. At the end of the process,

comparable acidity values for L. planarum BZ3 grown ina bioreactor and under static conditions were observed:219˚T and 214 ˚T, respectively.The statistical analysis of the two models (part of theresults are summarized in Table 1 and Table 2) showedthat the semi-empirical models used described thekinetics of the fermentation process extremelyaccurately, and their accuracy was comparable to theclassical kinetic models (data not presented). This wasconfirmed by the high correlation coefficient as well asby the low identification error of the model.According to the exponential model for strain L.delbrueckii ssp. bulgaricus TAB2, a relatively higherspecific growth rate was observed in its cultivation in thebioreactor (μ = 0.062 h-1) compared to the sameparameter during the static process (μ = 0.057 h-1). Factorα is about 30% higher in bioreactor cultivation,indicating increased biochemical activity in the cells dueto better stirring in the bioreactor compared to staticcultivation. This was due to the presence of dissolvedoxygen in the apparatus. It is well known that L.delbrueckii ssp. bulgaricus is the most sensitive lacticacid bacteria species in relation to oxygen, and in orderto overcome the presence of oxygen in the apparatus, theoxid-peroxide system of the cells is activated (Table 1).There was a similar trend in the cultivation of L.plantarum BZ3. Again, coefficient a was 22% higher,which also reflected the higher specific growth rate in thebioreactor cultivation (μ = 0.110 h-1) compared to thevalue of the same parameter during static cultivation (μ =0.103 h-1). The reason for the observed difference wasonce again the dissolved oxygen, but unlike its impact onstrains of the L. delbrueckii ssp. bulgaricus species, thepresence of oxygen had another impact on L. plantarumstrains. Although they do not contain the cytochromesinvolved in transferring electrons from the substrate tothe oxygen, these lactic acid bacteria are microaerophilic,and thanks to their flavoprotein systems, the flavoproteinoxidases, in particular, they can oxidize differentsubstrates in the presence of oxygen (Kwasnikov andNesterenko 1975). Probably, through its flavoproteinoxidases, L. plantarum BZ3 manages to incorporatedissolved oxygen as the terminal acceptor of electrons inthe oxidation of some substrates from the medium.Coefficient d in the exponential model showed theinfluence of the culture conditions on the rate of thebiochemical processes occurring in the cell. For bothstrains examined, higher values of this parameter wereobserved (2.263 for L.delbrueckii ssp. bulgaricus TAB2and 2.462 for L.plantarum BZ3) compared to the valuesof the same parameter during static cultivation (1.994 and2.218, respectively). The observed difference was a resultof the delayed diffusion of nutrients to the surface of thecell; slow diffusion of secreted metabolic products fromthe cell into the culture medium; uneven temperature andpH distribution throughout the culture medium that putthe microorganisms in the different microvolumes of themedium under different growth conditions. This was dueto the lower kinetic parameter values for the studiedstrains cultivated under static conditions.

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Figure 2: Dynamics of cultivation of Lactobacillus delbrueckii ssp. bulgaricus TAB2 and comparison of experimentaldata with kinetic models.

Figure 3: Dynamics of cultivation of Lactobacillus plantarum BZ3 and comparison of experimental data with kineticmodels.

From the results presented in Table 1 for the logisticcurve model, it can be seen that the relative andmaximum specific growth rates for the two strainsstudied were higher in their cultivation in the bioreactorcompared to static cultivation. For L. delbrueckii ssp.bulgaricus TAB2, μ = 0.108 h-1 and μm = 1.818 h-1 indynamic cultivation, and μ = 0.096 h-1 and μm = 1.637 h-

1 under static conditions. For L. plantarum BZ3, thevalues of these kinetic parameters when grown in abioreactor with mechanical stirring and under staticconditions were μ = 0.175 h-1 and μm = 1.719 h-1 and μ =0.156 h-1 and μm = 1.585 h-1, respectively.From the experimental data presented in Table 1, itappears that the exponential model yields lower relativegrowth rates for the two strains in their cultivation both

in the bioreactor and in the static process compared to thelogistic model.An analogous trend was also observed for the coefficientb in the logistic model showing the difference in theintensity of the biochemical processes occurring in thecells. For both strains tested, the value of this parameterwas higher in cultivation in a bioreactor than in staticcultivation: 0.956 and 0.725, respectively, for L.delbrueckii ssp. bulgaricus TAB2, and 0.739 and 0.649,respectively, for L. plantarum BZ3 (Table 1).The results on the lactic acid formation are alsointeresting. The data from Table 2 show that the type ofcultivation did not affect the degree of acid formation ofL. delbrueckii ssp. bulgaricus TAB2. In the cultivation ofthis strain under both dynamic and static conditions,almost the same acid formation rate was observed: q =

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0.0009 ºТ/cfu.cm3.h and q=0.0008ºТ/cfu.cm3.h,respectively. The same trend was evident for parameter δ

(Table 1). The value of δ indicates that the test strainproduced high amounts of lactic acid.

Table 1: Kinetic parameters of the empirical mathematical models used

* for logistic model

Table 2: Kinetic parameters of the Weibull model for the lactic acid formation kinetics of L. delbrueckii ssp.bulgaricus TAB2 and L. plantarum BZ3

Cultivationconditions Strain cm, ºТ c, ºТ q, ºТ/cfu.cm3.h δ R2 error

In the bioreactor L. delbrueckii ssp.bulgaricus ТАВ2

188 154 0.0009 2.61 0.9986 0.341Static 171 139 0.0008 2.62 0.9978 0.310

In the bioreactor L.plantarum BZ3 221 189 0.020 1.96 0.9965 0.264Static 219 187 0.037 2.64 0.9970 0.255

In L. plantarum BZ3, the type of cultivation method hadan effect on the degree of acid formation. Uponcultivation of the strain in a bioreactor, a sloweracidification rate of q = 0.020 ºТ/cfu.cm3.h and a lowervalue of δ = 1.96 was observed compared to the values ofthese parameters in static cultivation: q = 0.037ºТ/cfu.cm3.h and δ = 2.64.These results make it possible to conclude that thedissolved oxygen in the L.plantarum BZ3 cultivation inthe bioreactor had greater influence on acid formation,while in the L. delbrueckii ssp. bulgaricus TAB2,cultivation the dissolved oxygen did not affect the acidformation. This was the reason for the equalization of thetitratable acidity values at the end of the process duringL. plantarum BZ3 static and dynamic cultivation. Almostthe same amounts of lactic acid at the end of the twoprocesses were accumulated as a result of the moreintensive acid formation process under static conditions,although during the lag phase in static cultivation, aretention in the titratable acidity values followed by amore intensive process of acid formation was observed.

CONCLUSION

The present paper reviews a new approach to thedescription of the fermentation kinetics of lactic acidbacteria cultivation. For this purpose, semi-empiricaldependencies were used that allow the differentialequations of the fermentation process to be solvedanalytically and without the help of complexmathematical procedures for the identification of processparameters. The proposed model was applied to thedescription of the lactic acid process in the cultivation ofrepresentatives of the Lactobacillus delbrueckii ssp.bulgaricus and Lactobacillus plantarum species.Through the described process kinetics, it was shown thatthe presence of dissolved oxygen in the culture mediumled to differences in the cultivation process and hence tosubstantial differences in kinetic parameters. Theparameters of the proposed models also revealed

differences in the biochemical intensity of the processesoccurring in the lactic acid bacteria cells.

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Strain Empiricalmodel

Cultivation in bioreactor Static cultivationμ, h-1 a d (b*) R2 error μ, h-1 a d (b*) R2 error

L.delbrueckii ssp.bulgaricus TAB2

Exponential 0.062 0.953 1.994 0.9793 0.076 0.057 0.752 2.263 0.9701 0.070Logistic* 0.108 1.818 0.956 0.9706 0.065 0.096 1.637 0.725 0.9520 0.065

L.plantarum BZ3 Exponential 0.110 0.807 2.187 0.9828 0.065 0.103 0.658 2.462 0.9840 0.059Logistic* 0.175 1.719 0.739 0.9891 0.052 0.156 1.585 0.649 0.9840 0.059

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AUTHOR BIOGRAPHIESGEORGI KOSTOV is associated professor at the department“Technology of wine and beer” at University of FoodTechnologies, Plovdiv. He received his MSc in “Mechanicalengineering” in 2007, PhD on “Mechanical engineering in foodand flavor industry (Technological equipment in biotechnologyindustry)” in 2007 from University of Food Technologies,Plovdiv and DSc on “Intensification of fermentation processeswith immobilized biocatalysts”. His research interests are in thearea of bioreactors construction, biotechnology, microbialpopulation’s investigation and modeling, hydrodynamics andmass transfer problems, fermentation kinetics, beer production.

ZAPRYANA DENKOVA is professor at the department“Microbiology” at University of Food Technologies, Plovdiv.She received her MSc in “Technology of microbial products”in 1982, PhD in „Technology of biologically active substances“in 1994 and DSc on “Production and application of probiotics”

in 2006. Her research interests are in the area of selection ofprobiotic strains and development of starters for foodproduction, genetics of microorganisms, and development offunctional foods.

VESELA SHOPSKA is head assistant professor at thedepartment “Technology of wine and beer” at University ofFood Technologies, Plovdiv. She received her MSc in“Technology of wine and brewing” in 2006 at University ofFood Technologies, Plovdiv. She received her PhD in“Technology of alcoholic and non-alcoholic beverages(Brewing technology)” in 2014. Her research interests are in thearea of beer fermentation with free and immobilized cells; yeastand bacteria metabolism and fermentation activity.

ROSITSA DENKOVA-KOSTOVA is assistant professor atthe department “Biochemistry and molecular biology” atUniversity of Food Technologies, Plovdiv. She received herMSc in “Industrial biotechnologies” in 2011 and PhD in“Biotechnology (Technology of biologically activesubstances)” in 2014. Her research interests are in the area ofisolation, identification and selection of probiotic strains anddevelopment of starters for functional foods.

BOGDAN GORANOV is researcher in company “LBLact”,Plovdiv. He received his PhD in 2015 from University of FoodTechnologies, Plovdiv. The theme of his thesis was “Productionof lactic acid with free and immobilized lactic acid bacteria andits application in food industry”. His research interests are inthe area of bioreactors construction, biotechnology, microbialpopulation’s investigation and modeling, hydrodynamics andmass transfer problems, fermentation kinetics.

VASIL ILIEV is a service manager in “Weissbiotech”,Ascheberg, Germany. He received his PhD in 2016 fromUniversity of Food Technologies, Plovdiv. His researchinterests are in the area of bioreactors construction,biotechnology, microbial population’s investigation andmodeling, hydrodynamics and mass transfer problems,fermentation kinetics, beer and ethanol production.

DESISLAVA TENEVA is assistant professor at thedepartment of “Food Technologies” at Food Research andDevelopment Institute, Plovdiv. She received her MSc in“Analysis and Control of Food Products - University of FoodTechnologies – Plovdiv” in 2008 and PhD in “Microbiology(Biological sciences)” in 2017. Her research interests are in thearea of isolation, identification and selection of probiotic strainsand development of starters for functional foods.

PETAR NEDYALKOV is assistant professor at thedepartment “Technology of wine and beer” at University ofFood Technologies, Plovdiv. He received his PhD in“Technology of alcoholic and non-alcoholic beverages(Brewing technology)” in 2016. His research interests are in thearea of beer fermentation, non-alcoholic beverages productionand modeling of technological processes.

KRISTINA IVANOVA is assistant professor at thedepartment of “Food Technologies” at Food Research andDevelopment Institute, Plovdiv. She received her MSc in “FoodSafety - University of Food Technologies – Plovdiv” in 2014and PhD in “Food technologies” in 2018. Her research interestsare in the modeling of food technologies processes and use offood and beverages wastes for functional food development.