CELL CULTURE AND

852 Biotechnol. Prog. 2008, 24, 852À858 TOPICAL PAPERS: CELL CULTURE AND TISSUE ENGINEERING Effects of Glucose and Nitrogen Source Concentration on Batch Fermentation Kinetics of Lactococcus lactis Under Hemin-stimulated Respirative Condition Azher Razvi, Zisheng Zhang, and Christopher Q. Lan Dept. of Chemical and Biological Engineering, University of Ottawa, Ottawa, ON, Canada K1N 6N5 DOI 10.1021/bp.16 Published online in Wiley InterScience (www.interscience.wiley.com). Analytical solutions to the ordinary differential equations governing the kinetics of cell growth, substrate utilization, and product formation of batch fermentation processes were derived and used to study the kinetics of the hemin-stimulated respiratory cultivation of Lactococcus lactis at varied initial glucose concentrations and nitrogen source concentrations. Studies revealed that initial glucose concentration varying in the range of 60 to 90 g/L had no significant substrate inhibitive effect. Furthermore, elevating the concentration of complex nitrogen sources while maintaining glucose concentration at 60% led to a high final biomass concentration of 6.6 g/L, substantially higher than that obtained with the basic medium, which was 4.1 g/L. Keywords: Lactococcus lactis, hemin-stimulated, kinetics model, energy spilling Introduction Lactococcus lactis, among other lactic acid bacteria (LAB), are industrially important food-grade bacteria that have been extensively employed in food industry. It also has been employed for the production of nisin and other bacteriocins that are popular food preservatives.1–7 Bacteriocins are small antimicrobial peptides produced by bacteria with high specificity and efficacy against antibiotic-resistance bacterial pathogens and are regarded as a promising alternative antibacterial against antibiotic-resistant bacterial pathogens.8 Fine chemicals produced by the fermentation of L. lactis, such as lactic acid, diacetyl, and to a lesser extent, acetoin, are valuable products for the food and cosmetic industries.9 The status of L. lactis as a food-grade bacterium that has been safely used for centuries for the production and preservation of foods makes it an excellent platform for food-grade biotechnology applications. For instance, genetically engineered L. lactis strains are promising platforms for the production and delivery of live vaccines10–12 and other biopharmaceuticals. The poor growth characteristics of L. lactis, however, have been one of the major obstacles to the commercial adoption of L lactis for large-scale pharmaceutical production. The beneficial effects of hemin-stimulated respiration of L. lactis to cell growth was discovered by Sijpesteijn (1970) and confirmed by a series of studies conducted in late 1990s Correspondence concerning this article should be addressed to C. Q. Lan at christopher.lan@uottawa.ca. C V 2008 American Institute of Chemical Engineers and early 2000s.13–16 In a previous study, Lan et al.17 reported the pseudo-diauxic growth of L. lactis under heminstimulated respirative conditions. It was hypothesized that Lactococcus lactis generated bioenergy (ATP) through simultaneous lactate formation and hemin-stimulated respiration in the primary exponential phase, when glucose was abundant, and utilized lactate for cell growth and cell maintenance in the stationary phase, after glucose was exhausted. It was confirmed that supplementation of hemin to the medium, by allowing the remediation of the electronic chain, resulted in remarkable decrease of lactate production and increase of cell growth. The beneficial effects of heminstimulated respiration was further extended to the expression of recombinant proteins using L. lactis.18 A recent study19 on the effect of glucose concentration on the cell growth of L. lactis LM0230 under microaerobic conditions (5% DO) without hemin supplementation in the glucose concentration range of 13.75 mM (2.475 g/L) to 555 mM (99.9 g/L) revealed that, for batch fermentation, an initial glucose concentration of 138 mM (24.84 g/L) supported the highest specific growth rate and for fed-batch fermentation while the highest specific growth rate was obtained with the glucose concentration maintained at 55 mM (9.9 g/L). The glucostat experiments confirmed that the optimum glucose concentration was 55 mM and significant inhibition was observed when glucose concentration in the glucostat was increased to 277 mM (49.86 g/L), manifested by a 55% reduction of the glycolytic flux and almost identical reduction in the PFK (phosphate fructose kinase) activity. Another study conducted by the same group of researchers indicated Biotechnol. Prog., 2008, Vol. 24, No. 4 853 that under anaerobic conditions, both the cell growth and the nisin production were significantly inhibited when the initial glucose concentration of batch fermentations were higher than 35 g/L.20 However, in previous studies, we have observed significant improvement of cell growth of L. lactis at a glucose concentration of 60 g/L at microaerobic condition (DO 2%) when hemin was supplemented, i.e., when it conducted hemin-stimulated respiratory growth. It is therefore of interest to study the effects of glucose concentration on cell growth of L lactis under hemin-stimulated respirative condition. In this article, we report the effect of glucose concentrations in the range of 60–90 g/L on the kinetics of L. lactis IL 1403 under hemin-stimulated respiratory conditions, focusing on the primary exponential phase of the pseudo-diauxic growth of this bacterial species. Studies were also carried out to investigate the effects of elevated nitrogen source concentrations to the fermentation kinetics. Analytical solutions of three ordinary differential equation (ODE), i.e., the logistic equation for cell growth, the Pirt’s equation for substrate consumption, and the Leudeking-Piret’s equation for product formation, were developed and used to analyze the kinetic data obtained in these trials. has caused some controversy.22 Nevertheless, this equation has been widely used for characterizing the cell growth of various microorganisms in many fermentation systems.23,24 Interesting enough, its substrate independency is, in a sense, the very reason that makes it a versatile equation for describing batch cell growth kinetics. A typical batch cell growth curve of microbes is comprised of lag phase, exponential phase, transition phase, stationary phase, and death phase, and only in the transit phase, a rather short period in the whole cell growth profile, cell growth is substrate dependant. In other words, cell growth kinetics of a batch process cannot be characterized by a substrate-dependant model, e.g., the Monod equation or modified Monod equations, in most of the time of a batch process, although they may be excellent equation for application in describing a continuous process such as that in a Chemostat, where the existence of a limiting substrate is essential. On the other hand, although not directly depending on substrate concentration, the effects of initial substrate concentration and substrate concentration are reflected implicitly in the logistic equation by Xm, and the ratio X/Xm, respectively. When other parameters are constant, the initial substrate concentration determines the value of Xm and the substrate concentration is related to X/Xm. Substrate utilization A generalized mass balance on substrate reduces to the Pirt equation25 Development of Analytical solutions for Ordinary Differential Equations Governing Batch Fermentation Process Modeling of cell growth kinetics The Logistic equation is an empirical equation characterizing cell growth kinetics in terms of carrying capacity, which was borrowed from an ecological concept denoting the maximum achievable cell mass (population) a given environment can sustain.21 dS 1 dX ¼À M À ms X dt YX=S dt (5)   X lnet ¼ lm 1 À Xm (1) M where S (g/L) is the substrate concentration, YX/S (g DCW/g S) the maximum yield coefficient, and mS (g S/g DCW-h) the maintenance coefficient. Dividing Eq. 5 by Eq. 3 yields an equation describing the substrate utilization as a function of biomass concentration. where lm is the maximum specific growth rate (hÀ1), Xm the maximum biomass concentration that can be obtained with a particular cultivation system (strain, medium, and cultivation conditions),  corresponding to the maximum carrying  X capacity, and 1 À Xm the unused carrying capacity. The rate of cell growth is defined as dS 1 mS X m : ¼À M À dX YX=S kðXm À XÞ Integrating Eq. 6 between X0 and X yields (6) dX ¼ lnet X dt Combining Eqs. 1 and 2 yields S ¼ S0 À (2) 1 mS Xm Xm À X ln : M ðX À X0 Þ þ k Xm À X0 YX=S (7)   dX X ¼ lm X 1 À dt Xm (3) The analytical solution for Eq. 3, the ODE for modeling batch cell growth, has already been developed by integration21: Equation 7 represents a nonlinear relationship between X and S. Combining the logistic equation, i.e., Eq. 4 with Eq. 7 gives a relationship between substrate concentration (S) and M fermentation time (t). The parameters YX/S and mS can subsequently be estimated using a variety of nonlinear regression schemes. Product formation The classic Luedeking-Piret equation was developed in late 1950s for modeling product formation kinetics26 X¼ X0 elm t 1 À ð1 À elm t Þ X0 Xm (4) where X0 is the biomass concentration at t ¼ 0 h. The fact that the logistic equation is a substrate-independent equation dP dX ¼a þ bX: dt dt (8) 854 Biotechnol. Prog., 2008, Vol. 24, No. 4 Dividing Eq. 8 by Eq. 3 yields dP bXm ¼aþ kðXm À XÞ dX which, when integrated, yields (9) P ¼ P0 þ aðX À X0 Þ À bXm Xm À X ln k Xm À X0 (10) Similarly, this equation represents a nonlinear relationship between P and t when combined with the analytical solution of the logistic equation, Eq. 4. Performing a regression analysis to experimental data will yield coefficients a (g lactic acid/g DCW) and b (g lactic acid/g DCW-h), where a represents maximum product yield associated with cell growth, whereas b represents the product formation due to cell maintenance, which is not associated with cell growth. Figure 1. Typical batch cultivation of L. lactis under respirative conditions at 308C, pH 6.0, initial glucose 60 g/ L, 30% DO, and hemin 0.5 mg/L; (n) S, (~) P, and (^) X. Solid lines are best-fit curves of experimental data using corresponding models (i.e., cell growth, Eq. 4; product formation, Eq. 10; and substrate consumption, Eq. 7). Materials and Methods Microorganism L. lactis IL 1403 was kindly provided by Dr. Pierre Renault of INRA in France. Media The Basic Medium. The basic medium was modified from the commercial M-17 broth, containing 10.0 g/L yeast extract, 5.0 g/L peptone, 5.0 g/L tryptone, 1.0 g/L MgSO4Á7H2O, 5.0 mg/L hemin, and appropriate amount of glucose as specified in the text. The Enriched Medium. The enriched medium was modified based on the basic medium, with the concentrations of nitrogen sources, i.e., yeast extract, peptone, and tryptone increased by 50%. The composition of the enriched medium was therefore, 15.0 g/L yeast extract and, 7.5 g/L peptone, 7.5 g/L tryptone, 1.0 g/L MgSO4Á7H2O, 5.0 mg/L hemin, and appropriate amount of glucose as specified in the text. Inoculum Preparation. Stock cultures of Lactococcus lactis ssp. IL1403 were stored at À808C in 50% glycerol in a 1:1 (v/v) ratio. To activate the strain, 1 mL stock culture was melted and inoculated into a flask containing 100 mL basic medium which contains 10 g/L glucose. Flasks were incubated at 308C and 200 rpm for 12 h. Fermentation A 25-mL inoculum was used to inoculate NBS Bioflo 110 3-L stirred-tank bioreactors with a working volume of 1-L. Temperature, pH, and DO were controlled via a PI controller. An electrically powered heating jacket and cooling water flow were used to maintain the temperature throughout the fermentations at 308C. The pH was maintained at 6.0 with the addition of 5 M NaOH. DO was maintained at 30 % by sparging air at a rate of 0.5 L/min (i.e., 0.5 vvm), and varying agitation in the range of 200 to 600 rpm. Analytic procedures Samples of 1–3 mL were taken every 30 min over an 11-h period of fermentations. Optical density (OD) was measured using a ThermoElectron Gensys10 spectrophotometer at 600 nm. Samples were diluted to obtain an OD between 0.2 and 0.4. Samples were then clarified using 0.22-lm syringe filters. Glucose and lactic acid assays were performed on clarified samples using HPLC as described in a previous paper after diluting to appropriate dilution.17 Modeling The data obtained from the fermentations were modeled by minimizing the total sum square of the residuals for biomass, substrate, and product concentration X SSR ¼ X ðXe À Xp Þ2 þ X ðSe À Sp Þ2 þ X ðPe À Pp Þ2 (11) where subscript e denotes the experimental data and subM script p denotes the predicted data. Parameters k, YX/S, mS, a, b, and n in case of the modified form of the logistic equation were simultaneously varied using the solver function of Microsoft Excel 7.0 to minimize RSSR for all instances of modeling. Results Figure 1 shows the typical time courses of cell growth, glucose consumption, and lactic acid accumulation for L. lactis cultivation under hemin-stimulated respirative conditions. The batch was run at 308C, pH 6.0, and 30% DO. The initial glucose concentration was 60 g/L. As shown in Figure 1, cell growth under such conditions is modeled satisfactorily using the logistic Equation with a lm value of 1.0 hÀ1. The exponential phase started soon after inoculation without noticeable lag phase and lasted for about 3.5 h, followed by the deceleration phase. Cessation of growth appeared to be due to exhaustion of nutrients other than glucose because there was 5.0–10.0 g/L residual glucose left when cell growth leveled off. We speculate that the exhaustion of an essential growth factor such as amino acid or vitamin was Biotechnol. Prog., 2008, Vol. 24, No. 4 Table 1. Effects of Initial Glucose Concentration on Substrate Consumption Kinetics S0(g/L) lm (hÀ1) YMX/S (g DCW/g glucose) mS(g glucose/g DCW-h) YAPPX/S (g DCW/g glucose) a (g lactic acid/g DCW) b (g lactic acid/g DCW-h) YAPPP/X (g lactic acid/g DCW) YAPPP/S (g lactic acid/g glucose) 1.05 0.176 1.56 0.084 1.94 0.747 5.35 0.45 60 Æ Æ Æ Æ Æ Æ Æ Æ 0.02 0.005 0.14 0.001 0.05 0.02 0.08 0.02 0.95 0.179 1.64 0.080 2.25 0.842 6.35 0.51 80 Æ Æ Æ Æ Æ Æ Æ Æ 0.03 0.01 0.18 0.003 0.07 0.03 0.12 0.05 1.08 0.168 1.73 0.078 2.85 0.816 7.44 0.58 90 Æ Æ Æ Æ Æ Æ Æ Æ 855 0.03 0.02 0.15 0.002 0.09 0.01 0.05 0.03 M The maximum yield (YX/S) and maintenance coefficient (mS) were determined by fitting Eq. 7 and experimental data and the apparent biomass yield coefficient by equation YAPPX/S ¼ X/(S0 – S), where X is the average of the largest experimental biomass concentrations obtained with each individual set of conditions. Figure 3. Fermentation profiles for cell growth (^), glucose concentration (n), and lactic acid concentration (~) with enriched medium containing 60 g/L glucose. Figure 2. Experimental (data points) and model predictions (lines) of cell growth (top) and substrate concentration (bottom) with initial glucose concentrations of 60 g/L data (^), 80 g/L (n), and 90 g/L (l), respectively. the cause of growth cessation, which will be discussed later on in more detail. The kinetics of the accumulation of lactic acid exhibited typical kinetics of mixed-growth associated product with an a-value of 1.67 g lactic acid/g DCW and a b-value of 0.90 g lactic acid/g DCW-h. Modeling of lactate formation was satisfactorily performed using Eq. 10 with an R2 of 0.999. Substrate consumption kinetics was also modeled well using Eq. 7 with an R2 of 0.999. A maximum bioM mass yield coefficient (YX/S) of 0.20 g DCW/g glucose and a maintenance coefficient (mS) of 1.5 g glucose/g DCW-h were observed. The equation parameters summarized in Table 1 were the mean values of four parallel batches. The relative deviation of lm value, maximum biomass yield coefficient, maintenance coefficient, a value, and b value were 7.0, 2.8, 9.0, 9.8, and 29.3%, respectively. Figure 3 shows the kinetics of cell growth and substrate consumption in the basic medium with different initial glucose concentrations (i.e., 60, 80, and 90 g/L). For all glucose concentrations studied, the maximum OD was very close to each other, varied only between 12.0 and 13.0 (corresponding to a dry cell concentration fluctuating between 4.1 and 4.4 g/L). The value of lm determined by fitting experimental data to the logistic model (Eq. 4) was also with very small variation, changing between 0.95 and 1.05 hÀ1. Moreover, the net glucose consumptions in all three different initial glucose concentrations were also of insignificant differences, in the range of 50–55 g/L. Similarly, the maximum biomass yield coefficients were relatively constant, varying between 0.168 and 0.179 (Table 1). These results indicate that there was no significant substrate inhibition toward the growth of L. lactis when the initial glucose concentration was in the range of 60–90 g/L. Tolerance of L. lactis to such high glucose concentrations has not been reported before. The enhanced tolerance to glucose was most likely due to the beneficial effects of hemin to cell growth of L. lactis, which resulted in less lactate production by diverting metabolic flux away from lactic acid synthesis. It is clear from Figure 2 that cell growth stopped well before the exhaustion of glucose in all three tested initial concentrations of glucose in the range of 60–90 g/L. Given the facts that substantial quantities of residual glucose were left over in all the tests, it is logical to hypothesize that glucose was not the limiting factor under the investigated conditions. Experiments were carried out with the concentrations of yeast extract (YE), peptone (Pep), and 856 Biotechnol. Prog., 2008, Vol. 24, No. 4 Table 2. Kinetic Parameters Obtained with the Basic Medium and Enriched Medium at an Initial Glucose Concentration of 60 g/L Parameter lm (hÀ1) YAPPX/S (g DCW/g glucose) YMX/S (g DCW/g glucose) mS (g glucose/g DCW-h) YAPPP/X (g lactic acid/g DCW) a (g lactic acid/g DCW) b (g lactic acid/g DCW-h) GlucoseSufficient 1.00 0.084 0.18 1.56 5.35 1.94 0.75 GlucoseLimiting 1.20 0.109 0.18 1.23 3.88 2.55 0.47 tryptone (Trp) all increased by 50% while fixing the initial glucose concentration at 60 g/L. Figure 3 shows the experimental data and corresponding model fittings. As shown in Figure 3, the increase of the three complex nitrogen-source components resulted in a maximum OD of 19.0, corresponding to a dry cell concentration of 6.63 g/L and an increase of 60% over that obtained with the basic medium with less complex nitrogen source components. Furthermore, the termination of cell growth now corresponded to the exhaustion of glucose in this medium. It is interesting to note that the amount of lactate formed did not change significantly when compared to the batch at 60 g/L glucose with the basic medium. This seems to indicate that the extra glucose consumed due to the increased complex nitrogen sources was directed into the respiration pathways, leading to an increase in cell growth without producing more lactate. Discussion Limiting nutrient in the basic medium It has been well documented that L. lactis, as a member of the fastidious LAB, requires a large number of essential nutrients to grow. It was determined that the essential amino acids for L. lactis are glutamic acid, valine, methionine histidine, leucine, and isoleucine. Also essential to L. lactis growth are B group vitamins such as nicotinate, which is necessary for the synthesis of NAD(P) and pantothenate. Biotin, which is required for the synthesis of oleic acid and aspartic acid, and pyridoxal or pyridoxine, which is involved in the synthesis of several amino acids and which also acts as growth stimulant, are also essential growth factor to L. lactis. In total, L. lactis requires the inclusion of nine amino acids: glutamic acid, methionine, valine, leucine, threonine, arginine, isoleucine, histidine, and serine, and five vitamins: biotin, calcium pantothenate, nicotinic acid, pyridoxine, and riboflavin for cell growth.27–29 It is likely that one or more of the aforementioned growth factors became limiting in the course of fermentation when the basic medium was employed. Based on the results of the experiments with varied initial glucose concentrations shown in Figure 2, and the experiments carried out with the modified medium with increased concentrations of YE, Pep, and Trp (Figure 3), it can be concluded that (1) in the basic medium, cell growth was indeed limited by other nutrient apart from glucose, presumably from the list of essential growth factors that were previously described and (2) the increase of initial glucose concentration had no significant effect on the final biomass concentration, the maximum specific growth rate, or the maximum biomass yield coefficient, indicating that substrate inhibition in this range of glucose concentrations may not be significant. Dependency of maintenance coefficient on glucose concentration For heterotrophic organisms, the organic carbon sources are also utilized as energy sources for cell growth and cell maintenance. When the carbon source (in this study, glucose) is in excess, we have an energy sufficient system, which has been demonstrated to have very different kinetic characteristics than that of energy-limiting systems. In this study, as discussed previously, the basic medium was an energy-sufficient system because glucose was in excess. As shown in Table 2, when cultivated in the basic medium, the maximum biomass yield coefficient varied within a small range, i.e., between 0.167 and 0.179 DCW/g glucose, when the initial glucose concentration increased from 60 to 90 g/L and there was no apparent trend in the variation. It is interesting to note that the maximum biomass yield coefficients were typically twofold or greater than the respective apparent biomass yield coefficients, implying that a significant portion of glucose was utilized for cell maintenance rather than cell growth. On the other hand, the maintenance coefficient increased substantially from 1.56 to 1.73 g glucose/g DCW-h as initial glucose concentration increased from 60 to 90 g/L. This phenomenon can be explained by energy spilling. For heterotrophic cell growth, sugars serve as both carbon source and energy source. According to Pirt’s theory, the energy source consumed will generate bioenergy (ATP) for two functionalities, cell growth and cell maintenance. Maintenance energy represents the bioenergy (ATP) required for the physiological functions essential for maintaining cell viability. Some examples of these physiological functions include maintaining an energized membrane (i.e. a protonmotive force), transporting nutrients into the cell against chemical gradient (the positive transportation), maintaining optimal internal pH and osmotic pressure, maintaining cell motility, and repairing damage of subcellular structures.21 However, it has been established that the maintenance coefficient as defined by Pirt’s equation is a constant only when the system is energy-limiting (equivalent to glucose-limiting in this study). On the other hand, maintenance coefficient is a function of glucose concentration in an energy-sufficient system.30–32 Physiologically, energy-spilling may take place in a variety of ways. For instance, cells may reduce the efficiency of ATP generation, in an energy-sufficient condition, by means of deleting oxidative phosphorylation sites, branching the respiratory chain, and shifting metabolic pathways. Cells may also dispose intracellular energy by dissipation of membrane potential, ATP hydrolysis, and futile cycles. The dependency of maintenance coefficient on sugar concentration under energy-sufficient conditions is explained by a mechanism called energy spilling, reflecting the fact that energy is wasted without performing any essential physiological functions, in the form of partial uncoupling of catabolism from anabolism. The effect of energy spilling on maintenance coefficient was modeled by Tsai using a mechanistic model.32 As shown in Table 1, the a value increased significantly from 1.9 g lactic acid/g DCW at 60 g/L initial glucose concentration to 2.8 g lactic acid/g DCW at 90 g/L initial glucose concentration, whereas the b-value showed no significant change, varying between 0.75 and 0.82 g lactic Biotechnol. Prog., 2008, Vol. 24, No. 4 857 acid/g DCW-h. The increase of a value may be attributed to the saturation of the respiratory pathways by the glycolytic flux when glucose was in excess. As a consequence, the ‘‘excess’’ flux was diverted to lactate production via the pathway catalyzed by LDH.17 Indeed, it was reported that, when the flux through glycolysis was high, the ratio of NADH/ NADþ would also be high, favoring LDH activity.33,34 This could explain the higher lactic acid yield on biomass in the energy-sufficient system than that obtained in an energy-limiting system. However, it should be noted that these studies were carried out under anaerobic conditions, which is substantially different from the hemin-stimulated respiratory growth investigated in this study. Nevertheless, our results seem to confirm that such an analog is valid. Literature Cited 1. Amiali MN, Lacroix C, Simard RE. High nisin Z production by Lactococcus lactis UL719 in whey permeate with aeration. World J Microbiol Biotechnol. 1998;14:887–894. 2. Bromberg R, Moreno I, Delboni RR, Cintra HC, Oliveira PTV. Characteristics of the bacteriocin produced by Lactococcus lactis subsp. cremoris CTC 204 and the effect of this compound on the mesophilic bacteria associated with raw beef. World J Microbiol Biotechnol. 2005;21:351–358. 3. Cabo ML, Murado MA, Gonzalez MP, Pastoriza L. Effects of aeration and pH gradient on nisin production. A mathematical model. Enzyme Microbial Technol. 2001;29:264–273. 4. Fernandez De Palencia P, Nieto C, Acebo P, Espinosa M, Lopez P. Expression of green fluorescent protein in Lactococcus lactis. FEMS Microbiol Lett. 2000;183:229–234. 5. Fernandez A, Horn N, Gasson MJ, Dodd HM, Rodriguez JM. High-level coproduction of the bacteriocins nisin A and lactococcin A by Lactococcus lactis. J Dairy Res. 2004;71:216–221. 6. Wolf F, Traupe B, Takors A, Sauermann G, Hoppe U. A Novel Lantibiotic from Lactococcus lactis for the Treatment of Acne Vulgaris, J Invest Dermatol. 1997:108.657–657. 7. Yang R, Ray B. Factors influencing production of bacteriocins by lactic acid bacteria. Food Microbiol. 1994;11:281–292. 8. Parisien A, Allain B, Zhang J, Mandeville R, Lan CQ. Novel alternatives to antibiotics: Bacteriophages, bacterial cell wall hydrolases, and antimicrobial peptides. J Appl Microbiol. 2008; 104:1–13. 9. Boumerdassi H, Monnet C, Desmazeaud M, Corrieu G. Isolation and properties of Lactococcus lactis subsp. lactis biovar diacetylactis CNRZ 483 mutants producing diacetyl and acetoin from glucose. Appl Environ Microbiol. 1997;63:2293–2299. 10. Pacheco LGC, Zucconi E, Mati VLT, Garcia RM, Miyoshi A, Oliveira SC, De Melo AL, Azevedo V. Oral administration of a live Aro attenuated Salmonella vaccine strain expressing 14kDa Schistosoma mansoni fatty acid-binding protein induced partial protection against experimental schistosomiasis. Acta Tropica. 2005;95:132–142. 11. Piard JC. 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Glycolysis and the regulation of glucose transport in Lactococcus lactis spp. Effects of enhanced complex nitrogen concentration As shown in Table 2, most kinetic parameters, including those relevant to cell growth, substrate consumption, and product formation, were affected upon enriching the medium with 50% extra complex nitrogen sources, switching the medium from glucose-sufficient to glucose-limiting. It is interesting to note that the maximum biomass yield coefficient remained constant at 0.18 g DCW/g glucose. However, the apparent biomass yield coefficient increased significantly from 0.0836 to 0.11 g DCW/g glucose. This increase of apparent biomass yield coefficient can be explained by the elimination of energy spilling when glucose became limiting due to the elevated concentrations of other nutrients. Furthermore, the final biomass concentration also increased from 4.4 g/L with the basic medium to 6.6 g/L with the enriched medium. Conclusions Analytical solutions were developed for the ODEs governing cell growth kinetics (the logistic equation), substrate consumption kinetics (the Pirt’s equation), and production formation kinetics (the Luedeking-Piret equation) for batch fermentation processes. This set of equations were shown to be able to satisfactorily model the kinetics of the batch growth, glucose consumption, and lactic acid formation of L. lactis conducting hemin-stimulated respiration under both energy-limiting and energy-sufficient conditions. The study on batch fermentation kinetics of Lactococcus lactis IL1403 at varied initial glucose concentrations in the range of 60–90 g/L revealed that initial glucose concentration of up to 90 g/L was not inhibitive to cell growth, although profound influences upon the kinetic parameters decreased apparent biomass yield coefficient and increased maintenance coefficient were observed, which can be tentatively attributed to energy spilling when glucose was in excess. Modification of the medium by increasing the complex nitrogen-source components resulted in a substantial increase of the maximum biomass concentration and the maximum yield coefficient (YMX/S), leading to a high cell density culture of 6.6 g/L. Acknowledgment Financial support from NSERC (Natural Science and Engineering Research Council of Canada) is gratefully acknowledged. 858 lactis in batch and fed-batch culture. Microbial Cell Fact. 2007;6:16. Papagianni M, Avramidis N, Filiousis G. 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