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A mathematical model for gluconic acid fermentation by Aspergillus niger
Biochemical Engineering Journal 14 (2003) 137–141
Short communication
A mathematical model for gluconic acid fermentation by Aspergillus niger Jian-Zhong Liu a,∗ , Li-Ping Weng a , Qian-Ling Zhang b , Hong Xu b , Liang-Nian Ji a,∗ a
Biotechnology Research Center and Key Laboratory of Gene Engineering of Ministry of Education, Zhongshan University, Guangzhou 510275, PR China b Department of Chemistry and Biology, Normal College, Shenzhen University, Shenzhen 518060, PR China Received 3 July 2002; accepted after revision 25 September 2002
Abstract The fermentation kinetics of gluconic acid by Aspergillus niger were studied in a batch system. A simple model was proposed using the logistic equation for growth, the Luedeking–Piret equation for gluconic acid production and Luedeking–Piret-like equation for glucose consumption. The model appeared to provide a reasonable description for each parameter during the growth phase. The production of gluconic acid was growth-associated. © 2002 Published by Elsevier Science B.V. Keywords: Gluconic acid; Aspergillus niger; Kinetic model; Logistic equation; Luedeking–Piret equation
1. Introduction d-gluconic acid and its ␦-lactone are simple dehydrogenation products of d-glucose. Gluconic acid and its salts are important materials widely used in pharmaceutical, food, feed, detergent, textile, leather, photographic and concrete industries [1–3]. The future of a majority of these applications depends mainly on the commercial availability of gluconates. There are different approaches available for the production of gluconic acid, viz. chemical, electrochemical, biochemical and bioelectrochemical [4–6]. Fermentation has been one of the dominant routes for manufacturing gluconic acid at present [7]. Microbial species such as Aspergillus niger [8], Penicillium sp. [1], Zymomonas mobilis [9], G. oxydans [10] and Gluconobacter sp. [11,12] have been employed for gluconic acid production. In the fermentation medium, the accumulation of gluconic acids inhibits fungal growth. This results in lower yield of gluconic acid. To overcome this problem different methods of neutralization have been adopted [1,13–19]. A model is that describes relationships between principal state variables and explains quantitatively the behavior of a system. The model can provide useful suggestions for the analysis, design and operation of a fermenter. Fermentation models are normally divided into two classes: structured models where intracellular metabolic pathways are ∗ Corresponding authors. Fax: +86-20-8411015. E-mail address: [email protected] (J.-Z. Liu).
1369-703X/02/$ – see front matter © 2002 Published by Elsevier Science B.V. PII: S 1 3 6 9 - 7 0 3 X ( 0 2 ) 0 0 1 6 9 - 9
considered, and unstructured models where the biomass is described by one variable. Structured model seems complicated for normal use. Takamatsu et al. [20] reported the structured model to describe gluconic acid fermentation by A. niger. Unstructured models are much easier to use, and have proven to accurately describe many fermentations. Yet, to our knowledge, no investigations have been carried out on the unstructured model for gluconic acid production. In our previous paper, we reported zinc gluconate, magnesium gluconate and manganese gluconate production by fermentation [18,19]. In this study, experimental data from batch fermentations of gluconic acid by A. niger were examined in order to form the basis of kinetic model of the process.
2. Materials and methods 2.1. Micro-organism A. niger ZBY-7 [18,19,21,22], producing a high glucose oxidase and catalase activity, was used. The culture was maintained on malt agar slant at 4 ◦ C and subculture every 2 months. 2.2. Growth medium and conditions The fungus was grown in 500 ml Erlenmeyer flasks in 100 ml inoculum medium on a rotary shaker at 250 rpm
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Nomenclature mS P S S0 t X Xm X0 YX/S
maintenance coefficient (g substrate (g cells h)−1 ) sodium gluconate concentration (g l−1 ) substrate concentration (g l−1 ) initial substrate concentration (g l−1 ) ferment time (h) cell concentration (g l−1 ) maximum cell concentration (g l−1 ) initial cell concentration (g l−1 ) yield factor for cells on carbon substrate (g cells (g substrate)−1 )
Greek letters α growth-associated product formation coefficient (g g−1 ) β non-growth-associated product formation coefficient (g g−1 h−1 ) µm maximum specific growth rate (h−1 ) and 30 ◦ C for 24 h. The inoculum medium contains (g l−1 ): glucose, 50; KCl, 0.2; KH2 PO4 , 0.15; MgSO4 ·7H2 O, 0.12; (NH4 )2 HPO4 , 0.6; yeast extract, 3; peptone, 2. Sodium gluconate fermentation was carried out in the 5 l stirred tank bioreactor Biostat B (B. Braun Biotech International Diessel GmbH, Germany) with a working volume of 4 l. The bioreactor was equipped with two six-blade disc impellers (diameter of 64 mm). The following probes were installed on the top plate: METTLER TOLEDO sterilizable/autoclavable Inpro 6000 series O2 sensor (type: Inpro 6100/320/T/N), pH-electrode, pt-100-temperature sensor. The fermentation parameters were controlled by a digital measurement and control system. The fermentation medium consists of (g l−1 ): glucose, 100; KH2 PO4 , 0.35; urea, 0.55; MgSO4 ·7H2 O, 0.15. All media were sterilized at 121 ◦ C for 30 min. The fermentation conditions were as follows: agitation rate, 756 rpm; aeration rate, 0.9 vvm; temperature, 32 ◦ C; pH was controlled automatically at 6.0 by 40% (v/v) NaOH; peanut oil used as antifoam agent. The fermentation was inoculated with 10% (v/v) from a 24 h inoculum culture. 2.3. Analytical methods Samples were withdrawn twice at defined time. Fermentations were performed in duplicate culture, and analyses were carried out in duplicate. The data given here are the average of the measurements. The dry weights of mycelium were obtained after filtration of broth samples through preweighed filter discs. The harvested biomass was then washed with deionized water, dried for 8 h at 105 ◦ C, cooled in a desiccator and weighed. The concentration of gluconic acid was calculated by noting the amount of NaOH used to keep the pH value of liquid in the fermenter at 6.0. The amount of by-product acids, e.g.
citric acid, was assumed to be negligible compared with that of gluconic acid [23]. Residue glucose was determined by iodometry [21].
3. Kinetic model The model employs rate equations for biomass (X), sodium gluconate (P) and glucose (S) to describe the fermentation process. 3.1. Microbial growth The most widely used unstructured models for describing cell growth are the Monod kinetic model, the logistic equation and the haldane model. The logistic equation is a substrate independent model. It can finely describe the inhibition of biomass on growth, which exist in many batch fermentations [24]. The logistic equation can be described as follows: X dX (1) = µm X 1 − dt Xm The integrated form of Eq. (1) using X = X0 (t = 0) gives a sigmoidal variation of X as a function of t which may represent both an exponential and a stationary phase (Eq. (2)): X=
X0 Xm eµm t Xm − X0 + X0 eµm t
(2)
3.2. Product formation The kinetics of gluconic acid formation was based on the Luedeking–Piret equations. This model was originally developed for the formation of lactic acid by Lactobacillus delbrucckii [25]. According to this model, the product formation rate depends on both the instantaneous biomass concentration, X, and growth rate, dX/dt, in a linear manner: dP dX =α + βX dt dt
(3)
when α = 0, β = 0, the product formation is associate-growth. Thus, Eq. (3) can be changed to as follows: P = αX + k
(4)
3.3. Glucose uptake A carbon substrate such as glucose is used to form cell material and metabolic products as well as the maintenance of cells. The glucose consumption equation given below is a Luedeking–Piret-like equation in which the amount of carbon substrate used for product formation is assumed to be negligible: −
1 dX dS = + mS X dt YX/S dt
(5)
J.-Z. Liu et al. / Biochemical Engineering Journal 14 (2003) 137–141
Substituting Eq. (2) into Eq. (5) and integrating yields the following equation: X0 Xm eµm t X0 S = S0 − + µ t m YX/S (Xm − X0 + X0 e ) YX/S Xm mS Xm − X0 + X0 eµm t − ln µm Xm
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gluconic acid formation and cell concentration: P = −38.1 + 62.8X,
correlation coefficient r = 0.994 (7)
(6)
In this study, Eqs. (2), (4) and (6) are used to simulate the experimental results. The software Microcal Origin (Version 5.0, Microcal Software, MA0106, USA) was employed to estimate the values of parameters.
From the result, it can be seen that gluconic acid formation is strongly linearly related to cell growth. The result shows that the biosynthesis of gluconic acid can be attributed to a growth-associated type. In the model, α (62.8 g g−1 ) is the growth-associated product formation coefficient and may be identified with the product on biomass yield YP /X . k is equal to multiply α by X0 in numerical value. It denotes the level of gluconic acid resulted from the inoculums.
4. Results and discussion 4.3. Substrate uptake 4.1. Microbial growth Gluconic acid fermentation by A. niger showed a classical growth trend. After a lag phase (about 1–2 h), the cells entered the exponential growth phase. The strain started to form gluconic acid when the cells entered the exponential phase and therefore cell growth and gluconic acid production took place simultaneously. Taking Xm = 2.40 g l−1 from the experimental data, fitting the experimental data to Eq. (2) yields the values of parameters as follows: X0 and µm is 0.42 g l−1 and 0.22 h−1 , respectively. A comparison of calculated value of Eq. (2) with the experimental data is given in Fig. 1. The fitting of results was satisfactory. According to the fitted growth model, the calculated value of X0 (0.42 g l−1 ) was lower than that of the experimental value (0.55 g l−1 ). This can be perhaps attributed to the viability of cells. Less than 100% viability may yield an X0 value less than the measured initial cell concentration [26]. 4.2. Product formation After fitting the experimental data to Eq. (4), the following equation was used to describe the relationship between
By fitting the experimental data to Eq. (6), the values of parameters of glucose uptake model were as follows: YX/S , mS and S0 is 0.097 g g−1 , 3.73 g g−1 h−1 and 90.5 g l−1 , respectively. The fitting of results was satisfactory (Fig. 1). 4.4. Testing the model To test the microbial growth, product formation and substrate uptake models, a comparison of calculated value using the parameters evaluated above with another batch ferment experimental data is given in Fig. 2. Most of the errors were lower than 10%. It implies that these models can finely describe the gluconic acid ferment. In our previous paper [27], we reported that the above models were able to finely describe glucose oxidase production by A. niger. µm of glucose oxidase production (0.13 h−1 ) is lower than that of gluconic acid production. It may be because of low level of dissolved oxygen in glucose oxidase production in Erlenmeyer flask. Xm (6.92 g l−1 ) and YX/S (0.107 g g−1 ) of glucose oxidase production are higher than that of gluconic acid production. That is because CaCO3 is used as the agent of neutralization to control pH
Fig. 1. The comparison of experimental data and calculated values of biomass and glucose concentration of gluconic acid fermentation in 5 l fermenter: (䊏) experimental data of biomass; (䊉) experimental data of glucose concentration; (—) calculated value.
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Fig. 2. The comparison of experimental data in this work and calculated values of biomass, glucose and sodium gluconate concentration of gluconic acid fermentation in 5 l fermenter: (䊏) experimental data of biomass; (䊉) experimental data of glucose; (䊊) experimental data of sodium gluconate; (—) calculated value.
Fig. 3. The comparison of experimental data from Takamatsu et al. [20] and calculated values of biomass, glucose and sodium gluconate concentration of gluconic acid fermentation: (䊏) experimental data of biomass; (䊉) experimental data of glucose; (䊊) experimental data of sodium gluconate; (—) calculated value.
of broth in glucose oxidase production and CaCO3 is beneficial for cell growth and glucose oxidase production [21]. In the literature, several authors have studied gluconic acid production by A. niger, but only one paper gives enough information about system evolution so that a fitting to experimental data can be tried [20]. Data from Fig. 3 of Takamatsu et al. [20] have been fitted using the kinetic models described above. The model parameter X0 , Xm , µm , α, k, S0 , YX/S and mS was 0.01 g l−1 , 1.40 g l−1 , 0.33 h−1 , 67.1 g g−1 , −2.70 g l−1 , 40.0 g l−1 , 0.027 g g−1 and 0.36 g g−1 h−1 , respectively. The fitting results are satisfactory (Fig. 3). From these results, it can be seen that the parameters of logistic model and production format model of Takamatsu et al. data were similar with that of this work data. But the parameters of substrate consumption model of Takamatsu et al. data were all lower than that of this work
data. This may be because of different properties of strain used and culture conditions such as agitation and aeration. In addition, we can also find that the above model is invalid after the exponential growth phase.
5. Conclusions Fermentation is a very complex process, and it is often very difficult to obtain a complete picture of what is actually going on in a particular fermentation. The model presented in this work is able to fit not only the experimental data given in this work but also with those data from Takamatsu et al. [20]. One of the important limitations of this model is maximum biomass concentration (Xm ) since it was found experimentally. Therefore, in order to predict the
J.-Z. Liu et al. / Biochemical Engineering Journal 14 (2003) 137–141
parameter values of the model, an accurate value of Xm is required.
Acknowledgements We are grateful to the Natural Science Foundation of Guangdong Province for their financial support. References [1] A. Das, P.N. Kundu, Microbial production of gluconic acid, J. Sci. Ind. Res. 46 (1987) 307–331. [2] D.T. Sawyer, Metal–gluconate complexes, Chem. Rev. 64 (1964) 633–644. [3] P.E. Milsom, J.L. Meers, Gluconic and itaconic acids, in: M. Moo-Young (Ed.), Comprehensive Biotechnol, vol. 3, Pergamon Press, Oxford, 1985, pp. 681–700. [4] D.S. Rao, T. Panda, Comparative analysis of calcium gluconate and sodium gluconate techniques for the production of gluconic acid by Aspergillus niger, Bioprocess Eng. 8 (1993) 203–207. [5] J.M.H. Dirkx, H.S. van der Baan, The oxidation of glucose with platinum on carbon as catalyst, J. Catal. 67 (1981) 1–13. [6] C. Laane, W. Pronk, M. Franssen, C. Veeger, Use of bioelectrochemical cell for synthesis of (bio)chemicals, Enzyme Microb. Technol. 6 (1984) 165–168. [7] J. Bao, K. Furumoto, K. Fukunaga, K. Nakao, A kinetic study on air oxidation of glucose catalyzed by immobilized glucose oxidase for production of calcium gluconate, Biochem. Eng. J. 8 (2001) 91–102. [8] E.A. Gastrock, N. Porges, Gluconic acid production on pilot-plant scale, Ind. Eng. Chem. 30 (1938) 782–789. [9] S.L. Paterson, A.G. Fane, C.J.D. Fell, U.H. Chun, P.L. Rogers, Sorbitol and gluconate production in hollow fibre membrane reactor by immobilized Zymomonas mobilis, Biocatalysis 1 (1988) 217– 229. [10] N. Van Huynh, M. Decleire, A.M. Voets, J.C. Motte, X. Monseur, Production of gluconic acid from whey hydrolysate by Gluconobacter oxydans, Process Biochem. 21 (1986) 31–32. [11] W. Harmeier, A. Heinrichs, Membrane enclosed alginate beads containing Gluconobacter cells and molecular dispersed catalase, Biotechnol. Lett. 8 (1986) 567–572.
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[12] N.M.G. Oosterhuis, N.M. Groesbeek, A.P.C. Olivier, N.W.F. Kossen, Scale-down aspects of the gluconic acid production, Biotechnol. Lett. 5 (1983) 141–146. [13] P.N. Kundu, A. Das, Calcium gluconate production by a non-conventional method, Biotechnol. Lett. 4 (1982) 365–368. [14] R.H. Blom, V.F. Pfeifer, A.J. Moyer, D.H. Traufler, H.F. Conway, Sodium gluconate production–fermentation with Aspergillus niger, Ind. Eng. Chem. 44 (1952) 435–440. [15] A.J. Moyer, P.A. Wells, J.J. Stubbs, H.T. Herrick, O.E. May, Gluconic acid production, Ind. Eng. Chem. 29 (1937) 777–781. [16] M. Röhr, C.P. Kubicek, J. Kominek, Gluconic acid, in: H.J. Rehm, G. Reed (Eds.), Biotechnology, vol. 3, Verlag Chemie, Weinheim, 1983, pp. 155–156. [17] D.N. Shah, R.M. Kotharis, Fermentative production of injectablegrade calcium gluconate, Biotechnol. Prog. 7 (1991) 67–69. [18] L.-N. Ji, H.-Y. Yang, J.-Z. Liu, T.-B. Lu, N.-D. Wang, B.-H. Ye, The production of zinc gluconate by fermentation method by Aspergillus niger, Chinese Patent 94116330.X (1994). [19] L.-N. Ji, J.-Z. Liu, H.-Y. Yang, L.-P. Weng, The production of magnesium gluconate or manganese gluconate by fermentation method by Aspergillus niger, Chinese Patent 97114326.9 (1997). [20] T. Takamatsu, S. Shioya, T. Furuya, Mathematical model of gluconic acid fermentation by Aspergillus niger, J. Chem. Technol. Biotechnol. 31 (1981) 697–704. [21] J.-Z. Liu, Y.-Y. Huang, J. Liu, L.-P. Weng, L.-N. Ji, Effects of metal ions on simultaneous production of glucose oxidase and catalase by Aspergillus niger, Lett. Appl. Microbiol. 32 (2001) 16–19. [22] J.-Z. Liu, H.-Y. Yang, L.-P. Weng, L.-N. Ji, Synthesis of glucose oxidase and catalase by Aspergillus niger in resting cell culture system, Lett. Appl. Microbiol. 29 (1999) 337–341. [23] D.P.H. Hsieh, R.S. Silver, R.I. Mateles, Use of the glucose oxidase system to measure oxygen transfer rates, Biotechnol. Bioeng. 11 (1969) 1–18. [24] H. Gong, S. Lun, The kinetics of lysine batch fermentation, Chin. J. Biotechnol. 12 (Suppl.) (1996) 219–225. [25] R. Luedeking, E.L. Piret, A kinetic study of the lactic acid fermentation: batch process at controlled pH, J. Biochem. Microbiol. Technol. Eng. 4 (1959) 231–241. [26] M. Elibol, F. Mavituna, A kinetic model for actinorhodin production by Streptomyces coelicolor A3(2), Process Biochem. 34 (1999) 625– 631. [27] J. Liu, L. Weng, H. Yang, L. Ji, Mathematical models of simultaneous production of glucose oxidase and catalase by Aspergillus niger in Erlenmeyer flask, J. Chem. Ind. Eng. (China) 53 (1) (2002) 50–53.
Short communication
A mathematical model for gluconic acid fermentation by Aspergillus niger Jian-Zhong Liu a,∗ , Li-Ping Weng a , Qian-Ling Zhang b , Hong Xu b , Liang-Nian Ji a,∗ a
Biotechnology Research Center and Key Laboratory of Gene Engineering of Ministry of Education, Zhongshan University, Guangzhou 510275, PR China b Department of Chemistry and Biology, Normal College, Shenzhen University, Shenzhen 518060, PR China Received 3 July 2002; accepted after revision 25 September 2002
Abstract The fermentation kinetics of gluconic acid by Aspergillus niger were studied in a batch system. A simple model was proposed using the logistic equation for growth, the Luedeking–Piret equation for gluconic acid production and Luedeking–Piret-like equation for glucose consumption. The model appeared to provide a reasonable description for each parameter during the growth phase. The production of gluconic acid was growth-associated. © 2002 Published by Elsevier Science B.V. Keywords: Gluconic acid; Aspergillus niger; Kinetic model; Logistic equation; Luedeking–Piret equation
1. Introduction d-gluconic acid and its ␦-lactone are simple dehydrogenation products of d-glucose. Gluconic acid and its salts are important materials widely used in pharmaceutical, food, feed, detergent, textile, leather, photographic and concrete industries [1–3]. The future of a majority of these applications depends mainly on the commercial availability of gluconates. There are different approaches available for the production of gluconic acid, viz. chemical, electrochemical, biochemical and bioelectrochemical [4–6]. Fermentation has been one of the dominant routes for manufacturing gluconic acid at present [7]. Microbial species such as Aspergillus niger [8], Penicillium sp. [1], Zymomonas mobilis [9], G. oxydans [10] and Gluconobacter sp. [11,12] have been employed for gluconic acid production. In the fermentation medium, the accumulation of gluconic acids inhibits fungal growth. This results in lower yield of gluconic acid. To overcome this problem different methods of neutralization have been adopted [1,13–19]. A model is that describes relationships between principal state variables and explains quantitatively the behavior of a system. The model can provide useful suggestions for the analysis, design and operation of a fermenter. Fermentation models are normally divided into two classes: structured models where intracellular metabolic pathways are ∗ Corresponding authors. Fax: +86-20-8411015. E-mail address: [email protected] (J.-Z. Liu).
1369-703X/02/$ – see front matter © 2002 Published by Elsevier Science B.V. PII: S 1 3 6 9 - 7 0 3 X ( 0 2 ) 0 0 1 6 9 - 9
considered, and unstructured models where the biomass is described by one variable. Structured model seems complicated for normal use. Takamatsu et al. [20] reported the structured model to describe gluconic acid fermentation by A. niger. Unstructured models are much easier to use, and have proven to accurately describe many fermentations. Yet, to our knowledge, no investigations have been carried out on the unstructured model for gluconic acid production. In our previous paper, we reported zinc gluconate, magnesium gluconate and manganese gluconate production by fermentation [18,19]. In this study, experimental data from batch fermentations of gluconic acid by A. niger were examined in order to form the basis of kinetic model of the process.
2. Materials and methods 2.1. Micro-organism A. niger ZBY-7 [18,19,21,22], producing a high glucose oxidase and catalase activity, was used. The culture was maintained on malt agar slant at 4 ◦ C and subculture every 2 months. 2.2. Growth medium and conditions The fungus was grown in 500 ml Erlenmeyer flasks in 100 ml inoculum medium on a rotary shaker at 250 rpm
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Nomenclature mS P S S0 t X Xm X0 YX/S
maintenance coefficient (g substrate (g cells h)−1 ) sodium gluconate concentration (g l−1 ) substrate concentration (g l−1 ) initial substrate concentration (g l−1 ) ferment time (h) cell concentration (g l−1 ) maximum cell concentration (g l−1 ) initial cell concentration (g l−1 ) yield factor for cells on carbon substrate (g cells (g substrate)−1 )
Greek letters α growth-associated product formation coefficient (g g−1 ) β non-growth-associated product formation coefficient (g g−1 h−1 ) µm maximum specific growth rate (h−1 ) and 30 ◦ C for 24 h. The inoculum medium contains (g l−1 ): glucose, 50; KCl, 0.2; KH2 PO4 , 0.15; MgSO4 ·7H2 O, 0.12; (NH4 )2 HPO4 , 0.6; yeast extract, 3; peptone, 2. Sodium gluconate fermentation was carried out in the 5 l stirred tank bioreactor Biostat B (B. Braun Biotech International Diessel GmbH, Germany) with a working volume of 4 l. The bioreactor was equipped with two six-blade disc impellers (diameter of 64 mm). The following probes were installed on the top plate: METTLER TOLEDO sterilizable/autoclavable Inpro 6000 series O2 sensor (type: Inpro 6100/320/T/N), pH-electrode, pt-100-temperature sensor. The fermentation parameters were controlled by a digital measurement and control system. The fermentation medium consists of (g l−1 ): glucose, 100; KH2 PO4 , 0.35; urea, 0.55; MgSO4 ·7H2 O, 0.15. All media were sterilized at 121 ◦ C for 30 min. The fermentation conditions were as follows: agitation rate, 756 rpm; aeration rate, 0.9 vvm; temperature, 32 ◦ C; pH was controlled automatically at 6.0 by 40% (v/v) NaOH; peanut oil used as antifoam agent. The fermentation was inoculated with 10% (v/v) from a 24 h inoculum culture. 2.3. Analytical methods Samples were withdrawn twice at defined time. Fermentations were performed in duplicate culture, and analyses were carried out in duplicate. The data given here are the average of the measurements. The dry weights of mycelium were obtained after filtration of broth samples through preweighed filter discs. The harvested biomass was then washed with deionized water, dried for 8 h at 105 ◦ C, cooled in a desiccator and weighed. The concentration of gluconic acid was calculated by noting the amount of NaOH used to keep the pH value of liquid in the fermenter at 6.0. The amount of by-product acids, e.g.
citric acid, was assumed to be negligible compared with that of gluconic acid [23]. Residue glucose was determined by iodometry [21].
3. Kinetic model The model employs rate equations for biomass (X), sodium gluconate (P) and glucose (S) to describe the fermentation process. 3.1. Microbial growth The most widely used unstructured models for describing cell growth are the Monod kinetic model, the logistic equation and the haldane model. The logistic equation is a substrate independent model. It can finely describe the inhibition of biomass on growth, which exist in many batch fermentations [24]. The logistic equation can be described as follows: X dX (1) = µm X 1 − dt Xm The integrated form of Eq. (1) using X = X0 (t = 0) gives a sigmoidal variation of X as a function of t which may represent both an exponential and a stationary phase (Eq. (2)): X=
X0 Xm eµm t Xm − X0 + X0 eµm t
(2)
3.2. Product formation The kinetics of gluconic acid formation was based on the Luedeking–Piret equations. This model was originally developed for the formation of lactic acid by Lactobacillus delbrucckii [25]. According to this model, the product formation rate depends on both the instantaneous biomass concentration, X, and growth rate, dX/dt, in a linear manner: dP dX =α + βX dt dt
(3)
when α = 0, β = 0, the product formation is associate-growth. Thus, Eq. (3) can be changed to as follows: P = αX + k
(4)
3.3. Glucose uptake A carbon substrate such as glucose is used to form cell material and metabolic products as well as the maintenance of cells. The glucose consumption equation given below is a Luedeking–Piret-like equation in which the amount of carbon substrate used for product formation is assumed to be negligible: −
1 dX dS = + mS X dt YX/S dt
(5)
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Substituting Eq. (2) into Eq. (5) and integrating yields the following equation: X0 Xm eµm t X0 S = S0 − + µ t m YX/S (Xm − X0 + X0 e ) YX/S Xm mS Xm − X0 + X0 eµm t − ln µm Xm
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gluconic acid formation and cell concentration: P = −38.1 + 62.8X,
correlation coefficient r = 0.994 (7)
(6)
In this study, Eqs. (2), (4) and (6) are used to simulate the experimental results. The software Microcal Origin (Version 5.0, Microcal Software, MA0106, USA) was employed to estimate the values of parameters.
From the result, it can be seen that gluconic acid formation is strongly linearly related to cell growth. The result shows that the biosynthesis of gluconic acid can be attributed to a growth-associated type. In the model, α (62.8 g g−1 ) is the growth-associated product formation coefficient and may be identified with the product on biomass yield YP /X . k is equal to multiply α by X0 in numerical value. It denotes the level of gluconic acid resulted from the inoculums.
4. Results and discussion 4.3. Substrate uptake 4.1. Microbial growth Gluconic acid fermentation by A. niger showed a classical growth trend. After a lag phase (about 1–2 h), the cells entered the exponential growth phase. The strain started to form gluconic acid when the cells entered the exponential phase and therefore cell growth and gluconic acid production took place simultaneously. Taking Xm = 2.40 g l−1 from the experimental data, fitting the experimental data to Eq. (2) yields the values of parameters as follows: X0 and µm is 0.42 g l−1 and 0.22 h−1 , respectively. A comparison of calculated value of Eq. (2) with the experimental data is given in Fig. 1. The fitting of results was satisfactory. According to the fitted growth model, the calculated value of X0 (0.42 g l−1 ) was lower than that of the experimental value (0.55 g l−1 ). This can be perhaps attributed to the viability of cells. Less than 100% viability may yield an X0 value less than the measured initial cell concentration [26]. 4.2. Product formation After fitting the experimental data to Eq. (4), the following equation was used to describe the relationship between
By fitting the experimental data to Eq. (6), the values of parameters of glucose uptake model were as follows: YX/S , mS and S0 is 0.097 g g−1 , 3.73 g g−1 h−1 and 90.5 g l−1 , respectively. The fitting of results was satisfactory (Fig. 1). 4.4. Testing the model To test the microbial growth, product formation and substrate uptake models, a comparison of calculated value using the parameters evaluated above with another batch ferment experimental data is given in Fig. 2. Most of the errors were lower than 10%. It implies that these models can finely describe the gluconic acid ferment. In our previous paper [27], we reported that the above models were able to finely describe glucose oxidase production by A. niger. µm of glucose oxidase production (0.13 h−1 ) is lower than that of gluconic acid production. It may be because of low level of dissolved oxygen in glucose oxidase production in Erlenmeyer flask. Xm (6.92 g l−1 ) and YX/S (0.107 g g−1 ) of glucose oxidase production are higher than that of gluconic acid production. That is because CaCO3 is used as the agent of neutralization to control pH
Fig. 1. The comparison of experimental data and calculated values of biomass and glucose concentration of gluconic acid fermentation in 5 l fermenter: (䊏) experimental data of biomass; (䊉) experimental data of glucose concentration; (—) calculated value.
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Fig. 2. The comparison of experimental data in this work and calculated values of biomass, glucose and sodium gluconate concentration of gluconic acid fermentation in 5 l fermenter: (䊏) experimental data of biomass; (䊉) experimental data of glucose; (䊊) experimental data of sodium gluconate; (—) calculated value.
Fig. 3. The comparison of experimental data from Takamatsu et al. [20] and calculated values of biomass, glucose and sodium gluconate concentration of gluconic acid fermentation: (䊏) experimental data of biomass; (䊉) experimental data of glucose; (䊊) experimental data of sodium gluconate; (—) calculated value.
of broth in glucose oxidase production and CaCO3 is beneficial for cell growth and glucose oxidase production [21]. In the literature, several authors have studied gluconic acid production by A. niger, but only one paper gives enough information about system evolution so that a fitting to experimental data can be tried [20]. Data from Fig. 3 of Takamatsu et al. [20] have been fitted using the kinetic models described above. The model parameter X0 , Xm , µm , α, k, S0 , YX/S and mS was 0.01 g l−1 , 1.40 g l−1 , 0.33 h−1 , 67.1 g g−1 , −2.70 g l−1 , 40.0 g l−1 , 0.027 g g−1 and 0.36 g g−1 h−1 , respectively. The fitting results are satisfactory (Fig. 3). From these results, it can be seen that the parameters of logistic model and production format model of Takamatsu et al. data were similar with that of this work data. But the parameters of substrate consumption model of Takamatsu et al. data were all lower than that of this work
data. This may be because of different properties of strain used and culture conditions such as agitation and aeration. In addition, we can also find that the above model is invalid after the exponential growth phase.
5. Conclusions Fermentation is a very complex process, and it is often very difficult to obtain a complete picture of what is actually going on in a particular fermentation. The model presented in this work is able to fit not only the experimental data given in this work but also with those data from Takamatsu et al. [20]. One of the important limitations of this model is maximum biomass concentration (Xm ) since it was found experimentally. Therefore, in order to predict the
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parameter values of the model, an accurate value of Xm is required.
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