Batch cultures of supplemented whey permeate using Lactobacillus helveticus: unstructured model for biomass formation, substrate consumption and lactic acid production PDF

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Enzyme and Microbial Technology 28 (2001) 827– 834 www.elsevier.com/locate/enzmictec Batch cultures of supplemented whey permeate using Lactobacillus helveticus: unstructured model for biomass formation, substrate consumption and lactic acid production Abdeltif Amrane* Laboratoire des Procédés de ...

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Enzyme and Microbial Technology 28 (2001) 827– 834

www.elsevier.com/locate/enzmictec

Batch cultures of supplemented whey permeate using Lactobacillus helveticus: unstructured model for biomass formation, substrate consumption and lactic acid production Abdeltif Amrane* Laboratoire des Proce´de´s de Se´paration (Unite´ associe´e I.N.R.A.), Universite´ de Rennes I, Campus de Beaulieu, Baˆt.10A, 263 avenue du Ge´ne´ral Leclerc, CS 74205, 35042 Rennes cedex, France Received 15 July 2000; received in revised form 29 January 2001; accepted 1 March 2001

Abstract The Luedeking and Piret expression can not account for the cessation of production observed at the end of batch; so an empiric term has been previously added to this equation which accounted in a global way for possible substrate limitations. In the model developed in this work, a carbon substrate limitation appeared explicitly in the production expression. Assuming a sigmoidal variation with time of specific growth rate previously validated, the new production model matched well the entire experimental production kinetics. It has been successfully tested for a wide range of nitrogen supplementations, i.e. from an almost total coupling between growth and production for largely supplemented media, to a high decoupling in case of few available nitrogen. Since all the parameters of this model have an obvious biologic meaning, it may be an unvaluable tool for the comprehension of the phenomenon. The model accounted also well for the variation of the specific production rate versus specific growth rate, avoiding the noise due to the direct differentiation of experimental data. © 2001 Elsevier Science Inc. All rights reserved. Keywords: Lactic acid bacteria; Production kinetics; Model; Substrate limitations; Batch cultures

1. Introduction There is an interest in the economic utilization of the large quantities of cheese whey produced by the dairy industry, because of the environmental problem caused by its high organic matter content, due essentially to its lactose content [1,2]. This disaccharide can be fermented into lactic acid and this fermentation is still a matter of topical interest. This compound has significant applications in food, pharmaceuticals and cosmetics industries. Recently, new applications for lactic acid such as biodegradable plastics have accelerated research on its production as a bulk raw material [3–5]. For a better understanding of the fermentation process and its optimization, a model is of a great help [6 – 8]. Structured models have been reported to accurately describe the fermentation of lactose, glucose and galactose by Streptococcus cremoris [9 –11], but such a two-compartment model seems complicated for normal use. On the other hand, several unstructured models are available in the literature [8,12–14], * Tel.: 133-2-9928-2952; fax: 133-2-9928-2957. E-mail address: [email protected] (A. Amrane).

and have proven to accurately describe lactic acid fermentation in a wide range of experimental conditions and media. Owing to the large errors that can occur in differentiating experimental data [15], an integral method of analysis would be more suitable. Thus an unstructured model has been previously developed on the basis of the following assumptions [16]: The experimental kinetics of specific growth rate appeared to follow a complemented logistic function: 1 c.e d.t m 5 m max 11 m max 2 c

(1)

where x is the cellular concentration, and mmax, c and d are constants. Integration of Eq. (1) gave the following growth kinetic:

H

x 5 x0 z exp m max z t 2

F

GJ

m max mmax2c1c.ed.t In d mmax

(2) where x0 is the initial cellular concentration.

0141-0229/01/$ – see front matter © 2001 Elsevier Science Inc. All rights reserved. PII: S 0 1 4 1 - 0 2 2 9 ( 0 1 ) 0 0 3 4 1 - 6

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Nomenclature Subscripts ass: growth-associated cal: calculated exp: experimental max: maximum mod: model res: residual 0: initial A coefficient for growth associated production rate (dimensionless) B coefficient for non-growth-associated production rate (h21) c, d constant coefficients in growth model (both h21) F additional constant introduced in production model, Eq. (3) (h) p lactic acid concentration (g l21) PSY sensitivity of p to variations in a parameter y qp specific production rate (h21) s lactose concentration (g l21) t time (h) t1, t2 times when growth and production respectively cease (h) x biomass concentration (g l21) YP/S product on carbon substrate yield YP/X product on biomass yield YX/S biomass on carbon substrate yield YE yeast extract x2 statistically weighted sum of deviation squares m specific growth rate (h21)

In order to take into account the slowing down observed for production at the end of the fermentation, a corrective term has been introduced into the Luedeking and Piret [17] equation: dp dx 5 A z 1 B z x@1 2 e Fzm# dt dt

(3)

where p is the lactic acid concentration, A and B are the constants of the Luedeking and Piret equation, and F is an additional constant in the corrective term. Parameters A and B have an obvious biologic meaning, since they are the coefficients for growth- and non-growthassociated production, respectively, while the corrective term F has no self-evident biologic meaning. It has only been recently demonstrated that this empiric parameter accounted in a global way for peptidic limitations [8]. Indeed, the nutritional requirements of lactic acid bacteria and especially their nitrogen sources have long been considered complex [18 –20]; only part of the available peptides are metabolized [21], so a detailed nitrogen balance is very difficult to derive.

Therefore to improve the model, it would be interesting to take into account the kinetic of consumption of the limiting substrate, the carbon source, since from a previous work [22], it has been demonstrated that cessation of production always coincide with lactose exhaustion. This will be the aim of the present work.

2. Materials and methods 2.1. Microorganism Lactobacillus helveticus strain milano used throughout this work was kindly supplied by Dr. A. Fur (Even Ltd., Ploudaniel, France). Stock cultures were maintained on 10% (w z v21) skim milk and deep frozen at 216°C. As required, these cultures were thawed and reactivated by two transfers in 10% (w z v21) skim milk (42°C, 24 h). 2.2. Media Whey permeate powder (SIAB, Chateaubourg, France) was used as a carbon source; the powder was reconstituted at 57 g l21, corresponding to a lactose concentration of 48 g l21. Before use, permeate was clarified by a heat/calcium process [23]: it was supplemented with 3 g l21 CaCl2, 2 H2O, and pH was settled at 7.3; the solution was pumped through two heat exchangers at 80 and 16°C respectively (mean residence time: 20 s). The solution was left to decant overnight at 4°C, and supplemented with 20 g l21 yeast extract 1 5 g l21 of tryptic and pancreatic casein peptones (all these from Biokar, Pantin, France) for preculture medium and culture medium RM, and only 10 g l21 yeast extract for culture medium PM. 2.3. Culture conditions Bacteria were precultivated (9 h) on sterile preculture medium. Then 1600 ml of pasteurized culture medium were inoculated with 200 ml seed culture, and the reaction was processed at T 5 42°C. pH was maintained at 5.9 by automatic addition of 10 M NaOH; the mass of NaOH solution added for pH control was continuously recorded, allowing on-line calculation of lactic acid produced at each time point; the observed standard deviation was 6 1 g l21. In addition the fermentor was equipped with an aseptic recirculation loop (Watson-Marlow 101 FD/R peristaltic pump, Volumax, Montlouis, France) involving a laboratorymade turbidimeter. As turbidity was continuously recorded, total biomass was calculated on-line after dry weight calibration; the observed standard deviation was 60.2 g l21. The dry cellular weight of 100 ml of centrifuged and washed fermentation broth was measured after drying 2 h 1⁄4 under an infra-red light. At regular time intervals, samples were taken: total biomass were determined for turbidity calibration; on the su-

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pernatant, total lactic acid concentrations were determined spectrophotometrically by the Fe31 lactate complex method [24] for validation of the on-line measurements, and lactose concentrations by the phenol-sulphuric acid method [25], the observed standard deviation was 61 g l21. 2.4. Numerical methods From an experimental array [ti, yi, exp], i 5 1. . . . N, with y corresponding to the biomass x or the substrate s concentrations and an initial parameters vector P0 5 [x0, mmax, c, d]0 or [YP/S]0 for x and s respectively, the initial value for the target function x2 (statistically weighted sum of deviation squares) was calculated as follows: N

x2 5

O [D~y cal(i)]!

2

0

i51

2

(4)

i

The i-th term of the initial deviations vector D0 was D0 (i) 5 yi exp 2 yi, cal, where yi, cal was calculated by introducing ti and P0 in Eq. (2) for the biomass concentration x and by introducing pi, exp and P0 in Eq. (7) (see below) for the substrate concentration s. Then a “better” vector P1 (in the least squares sense) was drawn by a Levenberg-Marquardt algorithm [26]. Since no analytical solution was found for the production rate (Eq. (8), see below) the identification of parameters vector [A, B] was done by means of a Newton-Gauss algorithm [27]; involving a numerical integration (Runge-Kutta method) of the variational equation:

S D S D

­ dp d ­p 5 dt ­P ­P dt

(5)

The following definition have been used for the determination of the standard errors on the different parameters: SE~ y i! 5 6 t~ a ! z s z

Î C ii

(6)

with yi a growth, production or substrate consumption parameter; C the variance-covariance matrix; t the Student variable for a probability of 1-a 5 0.95 and a number of degrees of freedom of n (n 5 n 2 p), with n the number of experimental data points and p the number of parameters; and s the standard deviation on the experimental data points: SD2 s 5 , with SD2 the sum of the residual squares. n

Î

3. Results and discussion As shown in Figs. 1a and b, and as expected, RM medium resulted in a higher maximum biomass concentration (6.8 g l21 against only 4.0 g l21 on PM medium), as well as higher maximum growth and production rates: respectively 1.4 and 8.9 g l21 h21 on RM medium, and 0.8 and 4.1 g l21 h21 for PM medium. It should be noted that both media

Fig. 1. Growth (●), lactic acid production (‚) and lactose consumption () kinetics for L. helveticus cultivated on RM (a) and PM (b) media; (—) model.

differed by the quantity of available metabolizable nitrogen, higher for RM medium. As previously shown, lactic acid production ceased at the beginning of cell death for both media, since bacteria were unable to use the carbon content of autolyzed cells [22]; as expected this cessation of production was concomitant to the cessation of lactose consumption. Assuming that lactic acid and lactose concentrations were linearly correlated: Y P/S 5

P 2 p0 5 constant s0 2 s

(7)

the corrective term F in Eq. (3) has been replaced by an expression taking into account the substrate limitation:

F

G

dx s res dp 5Az 1Bzx 12 dt dt s

(8)

where s and sres were the lactose concentrations at time t and at the end of batch, respectively. As can be seen in Fig. 1a and b, and as expected [16], for both media Eq. (2) fitted the experimental data accurately until stationary state was achieved. The same conclusion held true for both substrate consumption and lactic acid production, which are accurately fitted by Eq. (7) and Eq. (8) respectively, on the whole culture, for both media. The signification of parameters c and d appeared in Fig. 2: the term mmax - c corresponded to the calculated maxi-

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Fig. 2. Schematic diagram for the specific growth rate kinetics.

mum specific growth rate and the maximum for the slope of the specific growth rate kinetics, which corresponded to a nil value for the second derivative, is a function of mmax, c and d. From Fig. 3a, and as assumed above, lactic acid production and lactose consumption were linearly correlated all along the culture, and the same yield YP/S was given by the model for both media within experimental error (Table 1); moreover linear regression of experimental data gave close values to that given by the model, respectively 0.84 and 0.82 for PM medium and 0.86 by both methods for RM medium. In the expression for the production rate [Eq. (8)], all the parameters have an obvious biologic meaning: the residual lactose concentration sres could be easily deduced from the lactose consumption kinetics, A and B were respectively the coefficients for growth- and non-growth associated production. From Table 1, and as previously observed [8], the parameter A increased and B decreased from 10 g l21 yeast extract (PM) to more largely supplemented medium (RM); on the latter medium, lactic acid production was almost totally coupled to growth since a nil value was obtained for the parameter B. In this case Eq. (8) could be simplified and analytically integrated: p 5 p o 1 A~ x 2 x o!

Fig. 3. Product on carbon substrate yield YP/S (a), biomass on carbon substrate yield YX/S (b) and product on biomass yield YP/X (c) for L. helveticus growing on RM (■) and PM ({) media; (—) model.

S H

p 5 p 0 1 A z x 0 z exp m max z t 2

F

z ln

m max d

m max 2 c 1 c z exp ~d z t! m max

GJ D 21

(10)

Owing to the constant product on substrate yield YP/S observed on both media, a constant yield biomass formed on substrate consumed YX/S was expected while net growth was recorded. This was confirmed at the examination of Fig. 3b:

(9)

By introducing Eq. (2) in Eq. (9), a fully associated production model could be easily derived:

Table 1 Optimal parameters obtained for growth, lactic acid production and lactose consumption data of batch cultures of L. helveticus cultivated on RM and PM media Parameters Medium RM Standard errorsa PM Standard errorsa a

x0 (g l21)

m max (h21)

c (h21)

d (h21)

Y P/S

s res (g 121)

A

B (h21)

0.24 0.06 0.33 0.04

0.63 0.12 0.49 0.05

0.0095 0.019 0.0021 0.0025

0.75 0.25 1.09 0.17

0.86 0.01 0.84 0.01

1.5 0.06 0.85 0.03

5.13 0.01 2.56 0.23

0.00 0.01 0.76 0.03

Standard errors for a probability of 0.95 and a number of degrees of freedom of 36 and 30 for RM and PM media respectively.

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it was the case until approximately 7 h and 6 h of culture on RM and PM media respectively, corresponding to 6.4 g l21 and 3.0 g l21 of cells formed, i.e. until nearly end of growth (7.4 h and 7 h on RM and PM media respectively). These yields YX/S were 0.16 for RM and 0.18 for PM medium, deduced from linear regression of experimental data. These close values for YX/S corroborate the above ones obtained for the yield YP/S since the sum of these two yields were close to unit for both media (1.02 and 1.00 for RM and PM media respectively). During the deceleration growth phase the yield YX/S decreased to a nil value at the beginning of the stationary phase and to a negative value during the decline phase. It has been previously demonstrated [22] that the best way to highlight the coupling between growth and production was to plot the lactic acid production vs. the biomass formed. This graph confirmed that growth and production were almost totally linked on RM medium (Fig. 3c). The product on biomass yield YP/X could be easily derived from the linear part of the curve; approximately the same values were given by the model and linear regression of the experimental data, respectively 5.1 and 5.2 for RM medium, and 4.3 and 4.5 for PM medium. By introducing Eq. (7) in Eq. (8), it came for the production rate:

F

dp s respY P/S dx 5Az 1Bzx 12 dt dt s 0pY P/S 2 ~ p 2 p 0!

G (11)

where s0 and p0 were the initial lactose and lactic acid concentrations, respectively. In this expression, the carbon substrate concentration did not appear, only constant parameters were needed: the initial and residual lactose concentrations, as well as the product on substrate yield YP/S. Indeed it has been demonstrated above (Fig. 3a) that, irrespective of the medium used, a constant value was recorded for the latter yield (0.85 6 0.02); initial and final lactose concentrations could be easily derived from chemical analysis of the medium and the final broth supernatant respectively. From this, previous batches [8,28] were analyzed by means of the new model. These runs were carried out on whey permeate supplemented with a range of yeast extract supplementations (2 to 30 g l21). Only the initial and final lactose concentrations were available, respectively 46 and 3 g l21 on average for all runs. From Fig. 4, the same final product concentration was recorded for all runs (36.5 6 0.1 g l21). This confirmed that for a given carbon source, irrespective of the nitrogen supplementation, a constant product on substrate yield is recorded. The slightly lower value for the final lactic acid concentration observed for this series of batches, if compared to those of this work (39.2 6 0.2 g l21), was due to the differences in the initial and final lactose concentrations, respectively 46 6 1 g l21 and 3 6 1 g l21 for the previous series of runs against 47.7 6 0.3 g l21 and 1.2 6 0.3 g l21 for this work. With the above values for s0 and sres, a constant product on substrate yield (0.85), and the optimal values for the growth

Fig. 4. Lactic acid production for L. helveticus growing on whey permeate supplemented with a range of yeast extract concentrations: (}), 2; (h), 5; (), 10; (‚), 20; (F), 30. (—) model.

parameters [8], from 5 to 30 g l21 YE the model matched well the production kinetics on the whole culture. For a slightly supplemented medium (2 g l21 YE), i.e. for a strong nitrogen limitation resulting in a high uncoupling between growth and production, the production model was less convenient, as also observed for the previously developed model [8]. The optimal set of parameters A and B are given in Table 2. A non negligible value for the parameter B for the highest YE supplementation (30 g l21) could be noticed, while on RM medium this parameter was nil (Table 1); however, it ...