Kinetics of Lactic Acid Fermentation Lactobacillus

March 3, 2019 | Author: Douglas Pereira | Category: Lactic Acid, Enzyme Kinetics, High Performance Liquid Chromatography, Fermentation, Sucrose
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J. Chem. T ech. Biotechnol . 1997, 68, 271 È 276

Kinetics of Lactic Acid Fermentation by Lactobacillus delbrueckii  Grown on Beet Molasses Jose   M. Monteagudo, * Lourdes Rodr • guez, Jesusa Rinco  n & Juan Fuertes Department of Chemical Engineering, University of Castilla-La Mancha, Campus Universitario, s/n, 13004 Ciudad Real, Spain (Received 13 February 1996; revised version received 29 July 1996; accepted 11 September 1996)

Abstract: The fermentation kinetics for the conversion of beet molasses, a valuable able and and econ econom omica icall ferm fermen enta tati tion on subs substr trat ate, e, to lacti lacticc acid acid by the the homo homo-fermentative organism L actobacillus delbrueckii C.E.C.T. 286 have been studied at controlled pH and temperature under anaerobic batch conditions. An inhibitory e†ect of lactic acid on fermentation of beet molasses has been found. The bacterium was able to produce lactic acid even after growth ceased. A kinetic model for the fermentation is proposed. From this model, the maximum allowable lactic acid concentration above which growth stops and the lactic acid level above which bacteria bacteria stop producing producing lactic acid were found to be 45 g dm ~3 and 57 g dm~3, respectively.

Key words: Lactic acid, fermentation kinetics, beet molasses, L actobacillus del brueckii

NOTATION A B K s m P P max [email protected] max S t X Y   [email protected] Y   [email protected] Y   [email protected]

SpeciÐc growth rate (h ~1) Maximum speciÐc growth rate (h~1)

k k max

Rate Rate cons consta tant nt (g lact lactic ic acid acid g~1 biomass) Rate constant (g lactic acid h~1) Monod constant (g dm~3) Coef Coeffi ficcient ient of maint ainteenanc nancee (g sucrose h~1 g~1 biomass) Lactic acid concentration (g dm~3) Lact Lactic ic acid acid conc concen entra trati tion on abov abovee which bacteria do not grow (g dm~3) Lact Lactic ic acid acid conc concen entra trati tion on abov abovee which which bacteria bacteria cease cease lactic lactic acid production duction (g dm~3) Substrate concentration (g dm~3) Time (h) Biomass concentration (g dm~3) Produc Productt yield yield on the utiliz utilized ed subsubstrate (g lactic acid g ~1 sucrose) Product yield on the formed biomass (g lactic acid g ~1 biomass) Biomas Biomasss yield yield on the utiliz utilized ed subsubstrate (g biomass g~1 sucrose)



Lactic acid is an industrially important product with a larg largee mark market et due due to its its attr attrac acti tive ve prop proper erti ties es.. For For example, the acid and salts are preferred to other acids in the the food food indu industr stry y beca becaus usee they they do not not domi domina nate te other Ñavors and also act as preservers. Furthermore, the the poss possib ibil ilit ity y of dire direct ctly ly conv conver erti ting ng lact lactic ic acid acid to acrylic acid1 has also turned lactic acid into an important raw material for the chemical industry. ReÐned sucrose, although expensive, is the substrate most commonly used for producing lactic acid by fermentation.2 Ho Howe weve ver, r, prod produc ucti tion on cost costss coul could d be reduced if sucrose from beet molasses was used instead, espec especial ially ly if the micro microorg organi anism sm could could produc producee lactic lactic acid directly from molasses, a valuable and economical fermentation substrate as a by-product of sugar manufactur facture. e. As report reported ed previo previousl usly, y,3,4 L actobacillu actobacilluss del brueckii C.E. C.E.C. C.T T 286 286 is one one of the the orga organi nism smss whic which h carries out the fermentation of molasses into lactic acid. Altho Although ugh the produc productio tion n of lactic lactic acid acid from from beet beet molasse molassess has been been studied studied by severa severall groups groups,,3 h 7 the deve develo lopm pmen entt of kine kineti ticc mo mode dels ls for for the the desi design gn and and

* To whom correspondence should be addressed.

271 0268-2575/97/$09. /$09.00 00 ( 1997 SCI. Printed Printed in Great Britain J. Chem. T ech. Biotechnol . 0268-2575/97


J. M. Monteagudo, L  . Rodr• guez, J. Rinco  n, J. Fuertes 2.3

Fig. 1. Schematic diagram of fermentation system used for the production of lactic acid by L actobacillus delbrueckii from beet molasses.

control of biochemical reactors has only been treated in one previous work,4 probably due to the complexity of  the process. Nevertheless, since the study of fermentation rates can be very useful for the design and control of both continuous and batch systems, in this paper the dynamic state of the batch fermentation of beet molasses has been expressed by three kinetic equations representing the concentrations of biomass, lactic acid and substrate in the batch culture of  L  . delbrueckii on beet molasses. To formulate these equations the major elementary mechanisms of the process were taken into account. In order to obtain the kinetic parameters of the model equations, batch fermentation experiments were performed at controlled pH and temperature under anaerobic batch conditions. Then, the experimental data were numerically analyzed and the kinetic parameters of the proposed equations evaluated. Although the mathematical model developed simpliÐes the true process, an adequate description of the fermentation kinetics of this system was provided. 2 2.1



L actobacillus delbrueckii C.E.C.T. 286, obtained from the Spanish Type Culture Collection, was used in all the fermentation experiments. The bacteria were kept frozen in a 20% (w/v) glycerol solution until ready for use. 2.2


Beet molasses (50% sucrose w/w) were diluted to obtain sucrose concentrations between 20 and 120 g dm~3. The medium was adapted from an optimum nutrient composition described previously.3

Inoculum preparation

The preparation of inoculum started with the transfer of  the frozen organisms to a 500 cm3 Erlenmeyer Ñask containing 250 cm3 of liquid MRS medium 8 containing (g dm~3) peptone, 10; yeast extract, 4; dextrose, 20; K HPO , 2 ; CH COONa . 3H O, 5 ; C H O (NH ) H, 2 4 3 2 6 5 7 42 2 ; MgSO . 7H O, 0É2 ; MnSO . 4H O, 0É05 and Tween 4 2 4 2 80, 10~3 dm3. The Ñask was subsequently incubated at 50¡C for 15 h, the time needed for the microorganism to reach the exponential growth phase. Then, 150 cm3 of  the growing biomass suspension was injected into the fermentor containing molasses medium to initiate the fermentation process. The organism concentration in the inoculum was 3 È11% (v/v), determined by centrifugation at 3200 rev min~1. 2.4

Batch equipment and procedures

All fermentations were performed under anaerobic conditions in a 5 dm3 stirred jar fermentor, shown schematically in Fig. 1. During the experiments, temperature and agitation rate were controlled at 49¡C and 100 rev min~1, respectively. The pH was maintained constant by automatic addition of 2 mol dm~3 NaOH solution. The total time of fermentation was approximately 26 h. The bacterial, sucrose and lactic acid concentrations were followed during the course of the fermentation. Samples were withdrawn at approximately 30 min intervals and analyzed immediately. 2.5

Analytical methods

Biomass was measured by constructing a calibration curve of optical density as a function of dry mass. Dry mass was determined by Ðltration of a suitable volume (4 È10 cm3, depending on the optical density) through a 0É45 km pore size membrane Ðlter (Millipore, Bedford, MA, USA), washing with distilled water, drying at 100¡C for 24 h and weighing. The optical density was measured on a Spectronic 20 D spectrophotometer at 620 nm. At the wavelength used the medium was found to have 100% transmission so changes in concentration did not a†ect optical density readings in the late stages of the fermentation. Sucrose concentrations were measured using a Gilson isocratic High Performance Liquid Chromatography System provided with an HPLC column for sugars (Spheri-5 Amino, Phase Sep, Connecticut, USA) and using CH CN ÈH O (77 : 23) as eluent. 3 2 Lactic acid concentration was measured using the same HPLC System but with a column for organic acids (Polipore H, Phase Sep, Conneticut, USA) using H SO (0É15 mol dm~3) as eluent. Acid production was 2 4 also measured by the amount of base (NaOH) added on demand to maintain the pH constant.

Kinetics of lactic acid fermentation by L. delbrueckii 3



Unstructured Batch Growth Models9 describe that the rate of increase in biomass is a function of the biomass only. Thus, dX /dt \ f  (X)


One of the simpler models belonging to the general form given by eqn (1) is MalthusÏ law, 9 which uses  f  (X) \ kX


where k is a constant. Thus, dX /dt \ kX


The speciÐc growth rate, k, is usually expressed as a function of the limiting substrate concentration, S, by a Monod-type relationship:9 k \ k [S /(K ] S)] max S


The Monod equation only applies to the growth phase and in the present case production of lactic acid diverts substrate and inhibition restricts growth. Therefore, eqn (3) must be extended to include the lactic acid concentration P, i.e. dX /dt \ kX(1 [ P / P




where k is a function of both substrate and product concentrations. Equation (5) predicts a continuous decrease of the growth rate as the product concentration rises. Furthermore, growth ceases at Ðnite product concentration, P . max In relation to the kinetics of product formation, the simplest kinetics arise when there is a simple stoichiometric connection between product formation and substrate utilization or growth. In this last case, the product formation rate, dP /dt, can be written as: dP /dt \ Y   dX /dt [email protected]

these models, production rate is proportional to biomass concentration rather than growth rate. The classic study of Luedeking and Piret10 on the lactic acid fermentation by L  . delbrueckii indicated that the product formation kinetics combined growthassociated and non growth-associated contributions:


The alcohol fermentation is an example of this class. Such product formation kinetics are sometimes called “growth-associatedÏ. In many fermentations, especially those involving secondary metabolites, signiÐcant product formation does not occur until relatively late in a batch cultivation, perhaps approaching or into the stationary phase. The penicillin fermentation exempliÐes such behaviour. Occasionally, a simple “non growth-associatedÏ model suffices for product formation kinetics in such cases. In

dP /dt \ A dX /dt ] BX


This two-parameter kinetic expression, often termed Luedeking ÈPiret kinetics, has proved extremely useful and versatile in Ðtting product formation data for many di†erent fermentations. However, since previous studies has demonstrated the inhibitory e†ect of lactate, by removal from the culture medium using dialysis, 11 this model may be improved by the addition of a term indicating dependence of the rate of acid production on inhibitor concentration, the lactic acid itself: dP /dt \ (A dX /dt ] BX)(1 [ P / [email protected]




According to this equation, dP /dt will become zero when P approaches [email protected] , the concentration greater than max P above which bacteria do not produce lactic acid. max Finally, substrate utilization kinetics may be expressed by an equation12,13 which considers both substrate consumption for maintenance and substrate conversion to biomass and product. The rate of substrate utilization is related stoichiometrically to the rates of formation of biomass and lactic acid. The substrate requirement to provide energy for maintenance is usually assumed to be Ðrst-order with respect to biomass concentration, mX. dS /dt \ [1/ Y   dX /dt [ 1/ Y   dP /dt [ mX [email protected]


[email protected]



To obtain the parameters of the equations that represent the concentrations of biomass, lactic acid and substrate in the batch culture of  L  . delbrueckii on beet molasses, batch runs (triplicate experiment) were performed under optimal conditions,3,7 as shown in Table 1. The data obtained from these experiments are shown in Fig. 2. They were Ðtted to eqns (5), (8) and (9) using a computer program that compared the batch fermentation data with the proposed rate expressions in such a way that the di†erence between the model predictions and the actual experimental values were minimized. To obtain the best Ðtting rate equations, a nonlinear regression analysis based on Marquardt Algorithm14 combined with a Runge ÈKutta method for di†erential equations was used. The estimated parameters are listed in Table 2.


J. M. Monteagudo, L  . Rodr• guez, J. Rinco  n, J. Fuertes

TABLE 1 Experimental Conditions for Batch Runs of  L  . delbrueckii Grown on Beet Molasses

Yeast extract concentration: Peptone concentration : Sucrose concentration : Temperature : pH : Agitation rate :

5 É31 g dm ~3 5 É08 g dm~3 65 g dm ~3 49¡C 5É90 100 rev min~1

Using data from the table, the ratio A / B equals 2É70. Compared with the value for A / B of 4É0 obtained by Luedeking and Piret10 in the lactic acid fermentation of  glucose by L  . delbrueckii, there is less growth-associated product formation in the present work. Further, the small value of the ratio A / B obtained here indicated the almost total independence of the lactic acid production rate from the growth rate. Bacteria produce lactic acid proportionally to the concentration, not depending on their growth phase. A low maintenance coefficient would thus be expected, 0 É09. The maximum speciÐc growth rate, k , was max 0É831 h~1. This result compared favorably with results obtained by Tyree et al .15 who found a maximum speciÐc growth rate of 0É722 h~1 for L actobacillus xylosus grown on glucose. The overall bacterial yield, Y   , had [email protected] a maximum value, 0 É270, at pH 5É90, a value higher than obtained by Hanson and Tsao16 in the fermenta-

tion of glucose Èyeast extract medium using L  . del brueckii. The maximum yield of lactic acid from sucrose (on beet molasses), Y   , was 0É91 g g~1, close to the [email protected] ized value of 0 É9 for all homofermentative lactobacilli 17 at a pH value of 5 É90. In Table 3, this parameter is compared with the yields obtained by other workers.16,18,19 The results from Hanson and Tsao16 and Luedeking18 agree with those obtained here, i.e. the yield increased up to pH values close to 5 É90. FinnÏs19 results, however, indicated that the highest yield occurred at lower pH values. The degree of reproducibility of the experimental system is shown in Fig. 2. The symbols represent the experimental data and the solid line the model predictions. The fermentations were characterized by a short lag phase followed by exponential growth and a simultaneous biosynthesis of lactic acid with growth. 4.1


Biomass production is presented in Fig. 2. The data show a marked decline in biomass concentration from about 15 h. This trend can be explained by including the possibility of endogeneous metabolism in the model. In endogeneous metabolism, reactions in bacteria consume bacterial material. An assumption often made for the appearance of the phase of decline (and sometimes also for the stationary phase) is that inhibitory products of metabolism accumulate during growth and their subsequent interaction with the viable organisms results in death. For the data obtained in the present study, eqn (5), which accounts for this, was found to accurately express the relationship between the biomass concentration and lactic acid concentration. From eqn (5) the maximum allowable lactic acid concentration above which bacteria do not grow, P , was predicted max to be 45 g dm~3. 4.2

Lactic acid

Fig. 2. Mathematical simulation of batch fermentations. (È), Theoretical model; (L sucrose, K lactic acid, = biomass) experimental data.

Similar to the analysis of biomass production, the dependence of the rate of lactic acid production on concentration was studied. Typical lactic acid concentra-

TABLE 2 Fermentation Parameters for L  . delbrueckii Grown on Beet Molasses

TABLE 3 Comparison of Lactic Acid Yields from Batch Fermentations

A (g lactic acid g~1 biomass) B (g lactic acid h~1) m (g sucrose h~1 g~1 biomass) (h~1) k max Y   (g cells g~1 sucrose) [email protected] Y   (g lactic acid g~1 sucrose) [email protected]

0É235 0É087 0É090 0É831 0É270 0É910



Y   [email protected] (this work)

Y   [email protected] (Ref . 16)

Y   [email protected] (Ref . 18)a

Y   [email protected] (Ref . 19)a

4É95 5É33 5É85 5É90

0É79 0É83 0É88 0É91

0É74 0É86 0É90 È

0É83 0É87 0É90 È

0É91 0É88 0É87 È



Kinetics of lactic acid fermentation by L. delbrueckii

tion curves are also presented in Fig. 2. The experimental data show that the lactic acid concentration at the end of the log phase (about 22 h) is approximately 57 g dm~3. The lactic acid had a noticeable e†ect on the growth rate at concentrations about 20 g dm~3. An expression for modelling inhibition due to lactic acid production is that derived from the Luedeking and Piret equation and given in the form of eqn (8). According to eqn (8), the lactic acid-producing capability of the bacteria was completely inhibited at a lactic acid concentration of 57 g dm~3 ([email protected] ). Thus, the model equamax tion was able to predict that bacteria were capable of  producing lactic acid even after growth ceases. Lactic acid is an inhibitor of both the growth of bacteria and its own biosynthesis. Figure 3 shows the e†ect of lactic acid on fermentation rate during batch fermentation with di†erent initial lactic acid concentrations. As the initial amount of lactic acid in the medium was increased, sucrose in the medium was consumed more slowly. When the initial concentration of lactic acid was 60 g dm~3, total inhibition occurred.



Substrate concentration curves are also illustrated in Fig. 2. Sugar was not completely utilized in the fermentations. The fermentations were considered complete when the sugar concentration dropped below 5 g dm~3. After this point, no biomass growth or lactic acid production was observed. For the sucrose concentration data obtained in the present study, eqn (9) was found to accurately express the relationship between the concentrations of substrate, biomass and lactic acid. From this equation, the sugar concentration at which bacteria did not grow and stopped producing lactic acid was found to be 4É85 g dm~3. As indicated above, eqn (9) is the sum of  three terms representing the growth of bacteria, the bio-

Fig. 3. E†ect of lactic acid concentration on growth rate and fermentation of  L  . delbrueckii grown on beet molasses (= : lactic acid, 20 g dm ~3 ; K : lactic acid, 40 g dm~3 ; L : lactic acid, 60 g dm~3).

275 synthesis of product and maintenance. A similar model was used to express the kinetics of substrate utilization in the lactic acid fermentation by S. cremoris12 and S. cerevisiae.13 5


Lactic acid, a product of industrial importance, can be produced by fermentation of the sucrose contained in beet molasses, a by-product of sugar manufacture. The experimental results obtained using beet molasses were similar to those obtained using synthetic sucrose solutions. Thus, lactic acid ready to use in the food industry may be obtained by fermentation of beet molasses, an economical fermentation substrate. The batch fermentation kinetics of this fermentation process were analyzed and two main conclusions derived. Firstly, lactic acid was an inhibitor of beet molasses fermentation. Secondly, bacteria were able to produce lactic acid even after growth ceased. To model the dynamic state of the batch fermentation three rate equations that represent growth, lactic acid production and sugar utilization have been proposed. The model has been found to provide an adequate description of the fermentation kinetics. REFERENCES 1. Martinez-Gonzalez, Y., Quiroz-Camacho, M. H., LedesmaPerez, A. S. & Jaramillo-Coronado, J. C., Production of lactic acid from pretreated molasses using L actobacillus delbrueckii. Rev. L at . Amer. Microbiol ., 30 (1988) 209 È14. 2. Vick Roy, T. B., Lactic acid. In Comprehensive Biotechnology, ed. M. Moo-Young. Pergamon, New York, 1985, Vol. 3, pp. 761 È76. 3. Monteagudo, J. M., Rincon, J., Rodriguez, L., Fuertes, J. & Moya, A., Determination of the best nutrient medium for the production of  L-lactic acid from beet molasses: a statistical approach. Acta Biotechnologica, 13(2) (1993) 103 È10. 4. Monteagudo, J. M., Production of lactic acid from beet molasses. PhD thesis, University of Castilla-La Mancha, Ciudad Real, Spain, 1993. 5. El-Sherbing, G. A., Rizk, S. S. & Yousef, G. S., Utilization of beet molasses in the production of lactic acid. J. Food Sci., 14 (1986) 91 È100. 6. Mossakowska, K., Laskowska, E. & Gozdek, K., Inoculation of highly pressed beet pulp with lactic acid acidforming bacteria. Gaz. Cukrow., 98 (1990) 13 È18. 7. Monteagudo, J. M., Rodriguez, L., Rincon, J. & Fuertes, J., Optimization of the conditions of the fermentation of  beet molasses to lactic acid by L actobacillus delbrueckii. Acta Biotechnol ., 14(3) (1994) 251 È 60. 8. De Man, J. C., Rogosa, M. & Sharpe, M. E., A medium for the cultivation of  L actobacilli. J. Appl . Bacteriol ., 23 (1960) 130 È5. 9. Bailey, J. E. & Ollis, D. F., Biochemical Engineering Fun damentals, 2nd Edn. McGraw-Hill, Singapore, 1986. 10. Luedeking, R. & Piret, E. L., A kinetic study of the lactic acid fermentation. J. Biochem. Microbiol . T echnol . Eng., 1 (1959) 393 È 430.

276 11. Friedman, M. R. & Gaden, E. L. J. R., Growth and acid production by L actobacillus delbrueckii in a dialysis culture system. Biotechnol . Bioeng., 12 (1970) 961 È74. 12. Aborhey, S. & Williamson, D., Modeling of lactic acid production by Streptococcus cremoris hp. J. Gen. Appl . Microbiol ., 23 (1977) 7 È21. 13. SaÐ, B. F., Rouleau, D., Mayer, R. C. & Desrochers, M., Fermentation kinetics of spent sulÐte liquor by Saccharomyces cerevisiae. Biotechnol . Bioeng., 28 (1986) 944 È 51. 14. Marquardt, D. W., An algorithm for least squares estimation of nonlinear parameters. J. Soc. Ind. Appl . Math., 2 (1963) 431. 15. Tyree, R. W., Clausen, E. C. & Gaddy, J. L., The production of propionic acid from sugars by fermentation

J. M. Monteagudo, L  . Rodr• guez, J. Rinco  n, J. Fuertes

16. 17. 18. 19.

through lactic acid as an intermediate. J. Chem. T ech. Biotechnol ., 50 (1991) 157 È 66. Hanson, T. P. & Tsao, G. T., Kinetic studies of the lactic acid fermentation in batch and continuous cultures. Biotechnol . Bioeng., 14 (1972) 233 È52. Gottschalk, G., Bacterial fermentations. In Bacterial  Metabolism. Springer-Verlag, New York, 1979, pp. 210 È 80. Luedeking, R., The lactic acid fermentation at controlled pH. PhD thesis, University of Minnesota, Minneapolis, 1956. Finn, R. K., The rate of formation of lactic acid by fermentation at controlled pH. PhD thesis, University of  Minnesota, Minneapolis, 1949.

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