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Power series kinetic model based on generalized stoichiometric equations for microbial production of sodium gluconate
Accepted Manuscript Title: Power series kinetic model based on generalized stoichiometric equations for microbial production of sodium gluconate Author: Xinchao Wang Xuefeng Yan Fei Lu Meijin Guo Yingping Zhuang PII: DOI: Reference:
S1369-703X(16)30150-4 http://dx.doi.org/doi:10.1016/j.bej.2016.05.009 BEJ 6476
To appear in:
Biochemical Engineering Journal
Received date: Revised date: Accepted date:
9-11-2015 17-5-2016 29-5-2016
Please cite this article as: Xinchao Wang, Xuefeng Yan, Fei Lu, Meijin Guo, Yingping Zhuang, Power series kinetic model based on generalized stoichiometric equations for microbial production of sodium gluconate, Biochemical Engineering Journal http://dx.doi.org/10.1016/j.bej.2016.05.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Power series kinetic model based on generalized stoichiometric equations for microbial production of sodium gluconate XinchaoWang,aXuefeng Yana*, FeiLub, MeijinGuob, YingpingZhuangb (a: Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology, Shanghai 200237, P. R. China b: State Key Laboratory of Bioreactor Engineering, East China University of Science and Technology, Shanghai 200237, P. R. China）
Corresponding author: Prof. Xuefeng Yan Email address: [email protected] Address: P.O. BOX 293, MeiLong Road 130, Shanghai, 200237, P. R. China Tel/Fax: +86-21-64251036
Highlights Power series kinetic model is developed for microbial production of sodium gluconate. The kinetic model is based on a generalized stoichiometric equations and a typical enzyme kinetic structure. The kinetic model can describe the fermentation process with sufficient accuracy. The kinetical model is simple.
Abstract Two main approaches are available for modeling of the fermentation process; these two are building an unstructured dynamic model and quantitative analysis of the metabolic network. The first one often employs several classic equations mostly derived from empirical knowledge and observation rather than mechanism knowledge. The second one is complicated because it requires sufficient biological information on cellular metabolic pathways. The objective of this article is to develop a kinetic model of the microbial production of sodium gluconate by using generalized stoichiometric equations and a typical enzyme kinetic structure called power series to overcome the shortcomings of previous methods.
The proposed kinetic model can describe the microbial growth of fungus as well as the interaction among dissolved oxygen, fungal metabolism, and product formation. Six batches were selected from seven batches of experimental sample data for modeling and analysis. The fitting precision was acceptable. The key parameters were analyzed based on the model. The main advantage of this model is that it has a simple structure based on the mechanism and can describe the fermentation process with sufficient accuracy. Keywords: fermentation; dynamic modeling; fungi; microbial growth; enzymes.
1. INTRODUCTION Sodium gluconate is an important material widely utilized as a firming,
stabilizing, or buffering agent in food, textile, pharmaceutical, and construction industries [1–3]. In recent years, it is also becoming a novel carbon source for fuels and chemicals production, such as ethanol production
[4-6]
. Many approaches for the
production of sodium gluconate are available, such as biochemical fermentation, electrochemical oxidation, homogeneous chemical oxidation and heterogeneous catalysis oxidation. At present, microbial production of sodium gluconate or fermentation by Aspergillus niger is the most preferred method [7–10]. The fermentation process can be modeled by two different models: structured models based on the analysis of metabolic pathways and unstructured models in which biomass is described by one variable. A structured model is difficult to build
[11]
because it requires sufficient
biological information on intracellular metabolic pathways. Two approaches can be applied to build a structured model. One involves establishing flow equilibrium equations based on the cellular metabolic network by using stoichiometric coefficients and selecting an objective for optimization
[12–13]
. The problem becomes a linear
optimization problem that fails to express many nonlinear features of the model. The other method involves kinetic analyses, such as enzyme kinetic analysis, metabolic control analysis
[14]
, and biochemical system theory [15].The problems include how to
guarantee feasibility, obtain sufficient constraints, and reduce computational difficulty. Unstructured models have simple forms. Previously proposed unstructured models can describe the fermentation process with satisfactory accuracy
[16]
. The
Monod equation and the logistic equation can be utilized to describe the growth trend of cells with different properties. The Luedeking–Piret and Luedeking–Piret/like equations can be used to describe production formation and glucose consumption. However, these classic equations are mostly derived from empirical knowledge and observation rather than mechanism knowledge. The proposed investigation approach attempts to combine structured and unstructured model features into a simple kinetic model that can describe the fermentation process with sufficient accuracy. Two main steps are required: describe the fermentation process through generalized stoichiometric equations and describe the relationship between reaction rate and metabolite concentration through the use of a power series structure. The parameters in the model can be categorized into two classes, namely, yield coefficients, which are determined by the structure of the generalized stoichiometric reactions, and kinetic rates, which are determined by specific metabolism pathways [17].
2. EXPERIMENTAL PROCEDURES 2.1 Microorganism The industrial strain for the production of sodium gluconate, Aspergillus niger (AN151) was supplied by Shan Dong Fuyang Biological Technology Co., Ltd.
2.2 Culture methods The A. niger strain was activated in a 250 mL flask (50 mL activation medium).
The activation medium slant inoculated with AN151 strain was incubated at 35 °C until it was covered with dense spores. The spores were harvested by washing the slant with 50 mL sterilized water. The formulation of the strain activation culture medium is 60.0 g/L glucose, 0.20 g/L urea, 0.13 g/L KH2PO4, 0.15 g/L MgSO4, 1.00 g/L corn steep liquor (Fu Yang Biology Co., Ltd., China), 5.00 g/L CaCO3, and 20.0 g/L agar. A total of 50 mL spore suspension was inoculated in a 15 L stirred bioreactor (9 L working volume) and cultivated for 18 h. Temperature and pressure were maintained at 38 °C and 0.1 MPa, respectively. The pH value was controlled at 5.5 by 7.5 M NaOH solution. Aeration and agitation rates were set to 0.8 vvm (air volume/culture volume/min) and 500 rpm, respectively. The formulation of the seed culture medium is 250 g/L glucose, 0.50 g/L KH2PO4, 1.80 g/L (NH4)2HPO4, 0.19 g/L MgSO4, 2.10 g/L corn steep liquor, and 0.20 mL/L polyether defoamer (Si Xin Scientific-Technological Application Research Institute Co., Ltd., Nanjing, China). A total of 4.5 L seeds were transferred into 50 L stirred bioreactor (30 L working volume). The pH, temperature, and pressure values during fermentation were similar to those during seed cultivation. Aeration and agitation rates were set to 1.2 vvm and 550 rpm, respectively. The fermentation ended when the glucose concentration was lower than 3 g/L. The formulation of the fermentation culture medium is 330 g/L glucose, 0.55 g/L KH2PO4, 0.40 g/L (NH4)2HPO4, 0.20 g/L MgSO4, and 0.20 mL/L polyether defoamer. All the culture media were sterilized at 115 °C for 20 min, and their initial pH
were adjusted to 7.0 by using 1 M NaOH solution, so that gluconic acid can turn into sodium gluconate.
2.3 Analytical methods Glucose concentration was measured with a hexokinase-glucose 6-phosphate dehydrogenase assay kit (Shanghai Ke Xin biotech Co., Ltd., China). Gluconic acid (GA) was quantitatively analyzed through high-performance liquid chromatography (HP 1100; Agilent) at 210 nm. AC18-H column (4.6 × 250 mm; Sepax) was utilized. The flow rate was set to1 mL/min. Elution was implemented with 3 M methanol solution and 0.25 M phosphate solution (1:1). The column temperature was maintained at 28 °C. Cell growth was monitored by measuring dry mycelia weight (DCW). A total of 50 ml fermentation broth was filtered through a filter membrane (0.45 µm). The cells were washed twice with distilled water, dried at 105 °C for 36 h, and equilibrated at room temperature in a desiccator. Dissolved oxygen was measured with Mettler electrode.
3. POWER SERIES KINETIC MODEL BASED ON GENERALIZED STOICHIOMETRIC
EQUATIONS
FOR
SODIUM
GLUCONATE
PRODUCTION To model the fermentation process, the following four main procedures need to be implemented [18–23].
(1) Determination of generalized stoichiometric reactions (2) Determination of the kinetic structure of the reaction rates (3) Establishment of dynamic models of the fermentation process (4) Determination of the model parameters
3.1 Hypothesis about generalized stoichiometric equations We assumed that three main generalized stoichiometric equations are involved in the fermentation process; these three are expressed as 𝑟1
S + X → X, 𝑟2
C + S + X → 𝐻2 𝑂 + 𝐶𝑂2,
(1)
𝑟3
C + S + X → P, Where 𝑟𝑖 stands for the rates of the generalized stoichiometric reactions; X denotes biomass concentration in g/L; S denotes substrate concentration, which stands for glucose, in g/L; P is a notation of produced sodium gluconate in g/L; and C denotes dissolved oxygen tension in %. In the equations, reaction 1 describes cell growth and can be regarded as a self-catalyzed reaction. Reaction 2 describes cell metabolism and is a full oxidation process. Reaction 3 describes product formation, in which oxygen, substrate, and enzyme are the three main reactants [24–25].
3.2 Hypothesis about models of reaction rates For each rate of the generalized stoichiometric reactions, a power series structure
was utilized as follows: 𝑟1 = 𝑆𝑘1 ∗ 𝑋𝑘2 , 𝑟2 = 𝑆𝑘3 ∗ 𝐶𝑘4 ∗ 𝑋𝑘5 ,
(2)
𝑟3 = 𝑆𝑘6 ∗ 𝐶𝑘7 ∗ 𝑋𝑘8 , Where 𝑘𝑖 denotes the parameters obtained by simulation and optimization that only depend on metabolic properties; 𝑟𝑖 denotes the rates of the generalized stoichiometric reactions.
3.3 State space equations Based on the previous assumption, the state space equations describing the kinetics of the fermentation process are as follows: d𝒁 dt dC dt
= 𝑲𝒓,
(3)
= 𝐶(𝑡),
Where 𝒁𝐓 = [𝑋, 𝑃, 𝑆]𝑇 is the state space vector, 𝑟 𝑇 = [𝑟1 , 𝑟2 , 𝑟3 ]𝑇 is the vector of kinetic rates, t is time, and 𝑲 is the matrix of yield coefficients. 𝑘9 𝑲=[ 0 −𝑘13
−𝑘10 0 −𝑘14
−𝑘11 𝑘12 ] −𝑘15
(4)
In reactions 2 and 3, X only stands for enzymes produced by cells, so modification can be obtained as 𝑘10 = 𝑘11 = 0. For
dC dt
, the situation is rather complicated. Hence, we used a quadratic curve
fitting of t to describe the oxygen change rate temporarily. And for 𝐶(𝑡), it was obtained in each batch.
3.4 Optimization After establishing the state space equations, the model parameters were obtained through nonlinear optimization. To achieve high accuracy, relative error was selected as the optimization objective. Min = ∑3𝑖=1 𝑅𝐸𝑖 ,
(5)
𝑦𝑖_𝑝𝑟𝑒𝑑 −𝑦𝑖_𝑒𝑥𝑝
1
𝑅𝐸𝑖 = 𝑛 ∑𝑛𝑗=1 |
𝑦𝑖_𝑒𝑥𝑝
|,
Where n stand for the total amount of sample data, 𝑦𝑖_𝑝𝑟𝑒𝑑 and 𝑦𝑖_𝑒𝑥𝑝 stand for the predicted value and experimental data of the ith state variable respectively. The optimization problem was solved with the modified DE algorithm Alopex-DE[26]. Detailed information on this modified algorithm is available elsewhere and will not be discussed further in this paper.
4. RESULTS AND DISCUSSION 4.1 General performance To analyze the accuracy of the kinetic model, several evaluation indices were adopted. We selected root mean squared error (RMSE) and relative error (RE) as the evaluation indices. 2 ∑𝑛 𝑖=1(𝑦𝑝𝑟𝑒𝑑 −𝑦𝑒𝑥𝑝 )
RMSE = √ 1
𝑛 𝑦𝑝𝑟𝑒𝑑 −𝑦𝑒𝑥𝑝
RE = 𝑛 ∑𝑛𝑖=1 |
𝑦𝑒𝑥𝑝
|
(6)
Figure 1. Fitting results for batch 1.
Figure 2. Fitting results for batch 2.
Figure 3. Fitting results for batch 3. Figs 1 to 3 show the fitting results for each batch. We can see that the model is roughly in line with the experimental data, and the RMSE and RE of the model for each variable in three batches are shown in Tables 1 and 2. Table 1.RMSE of the model for each variable in three batches Fermentation batches
X
P
S
C
Batch 1
0.006
0.9367
0.5696
3.9198
Batch 2
0.0109
0.8227
0.5775
2.6368
Batch 3
0.0197
1.3609
0.8085
2.7704
Table 2.RE of the model for each variable in three batches Fermentation batches
X
P
S
C
Batch 1
0.0603
0.0841
0.048
0.0477
Batch 2
0.1021
0.0623
0.0345
0.0273
Batch 3
0.0692
0.0291
0.0523
0.0337
The parameters were obtained for the model as below. Batch 1 to 3 use the same set of parameters. Table 3. Parameters of the model 𝑘1
𝑘2
𝑘3
𝑘4
𝑘5
𝑘6
𝑘7
1.7406
0.8512
0.5137
0.494
1.2494
-0.1141
0.3359
𝑘8
𝑘9
𝑘12
𝑘13
𝑘14
𝑘15
0.4196
0.0003
1.4391
0.0209
-0.0801
1.1568
4.2 Microbial growth The cells in the fermentation process exhibited a typical growth trend. The cells entered the exponential growth phase, which lasted for more than 10 h, and then the stationary phase. The strain began to produce sodium gluconate as soon as the cells entered the exponential phase. Because even the strain was at a low density, the enzyme produced by the strain, such as glucose oxidase and lactonase, can still be sufficient for glucose use in product formation when there exits sufficient dissolved oxygen. The initial trend of cell growth was similar to that of sodium gluconate production.
4.3 Product formation The results also reveal that sodium gluconate is not related to cell growth in the stationary phase. In this phase, the enzyme for product formation produced by the strain changed slightly, so the constraints probably transferred from enzyme to
substrate concentration and oxygen concentration.
4.4 Substrate and oxygen uptakes Substrate uptake is related to oxygen uptake. Based on the generalized stoichiometric equations established previously, this phenomenon is reasonable. In particular, when cells entered the stationary phase, the activity of reaction 1 is low, so substrate and oxygen uptakes seemed more related.
5. ANALYSIS OF THE KEY PARAMETER WITH THE MODEL Some important factors were found during the optimization of the fermentation techniques. Dissolved oxygen is one of them, so we consider that it is a key parameter on the fermentation process. To analyze it, the determined model was utilized to predict the value of three state variables (biomass, glucose, sodium gluconate) under a different condition. The fermentation techniques of batch 4 to 6 are a lot different from that of batch 1 to 3. So it was selected that the model whose parameters were determined by optimization with experimental data from batch 4 and used the experimental data of initial time from batch 5 and 6 for prediction.
Figure 4. Prediction results under the condition of low dissolved oxygen for batch 5.
Figure 5.Prediction results under the condition of low dissolved oxygen for batch 6.
According to Figs 4 and 5, it can be seen that when the dissolved oxygen is not controlled at the same level as the batches before, the results are also different from the ones before. In these two batches, the dissolved oxygen is controlled at a low level by mainly changing the air inflow and agitation rate. As the experimental results are shown, when dissolved oxygen declines rapidly, product formation deteriorates, glucose uptake remains similar, and mycelium also drops. The prediction made by the model is quite well. In this way, the experimental results and the model both indicate that the dissolved oxygen is both important to microbial use and product formation use, and also prove that dissolved oxygen is a key parameter in the fermentation
process for sodium gluconate.
6. CONCLUSIONS A power series kinetic model based on generalized stoichiometric equations for microbial production of sodium gluconate was developed. Compared with unstructured dynamic models with several classic mechanism equations, the proposed model can better describe the growth of fungus and the interaction among dissolved oxygen, fungal metabolism, and product formation. Compared with structured models based on the analysis of metabolic pathways, the proposed model is easier to build, and the three generalized stoichiometric equations describe the substrate uptake of different uses separately, which reflects the intracellular metabolic pathways clearly. Each generalized stoichiometric equation used is based on the power series, which divides the model parameters into two types. Thus, the model combines known biological mechanism with simplicity. The fitting precision of the model is acceptable.
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] Fan Z, Wu W, Hildebrand A, et al. A Novel Biochemical Route for Fuels and
Chemicals Production from Cellulosic Biomass. Plos One. 7 (2012) e31693. [5] Wu W, Fan Z. A general inhibition kinetics model for ethanol production using a novel carbon source: sodium gluconate. Bioprocess and Biosystems Engineering. 36 (2013) 1631–1640. [6] Wu W H. Fuel ethanol production using novel carbon sources and fermentation medium optimization with response surface methodology. International Journal of Agricultural and Biological Engineering. 6 (2013) 42–53. [7] 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. [8] 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. [9] C. Laane, W. Pronk, M. Franssen, C. Veeger, Use of bioelectrochemical cell for synthesis of (bio)chemicals, Enzyme Microb. Technol. 6 (1984) 165–168. [10] 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. [11] Chassagnole C, Noisommit-Rizzi N, Schmid J W, et al. Dynamic modeling of the central carbon metabolism of Escherichia coli.. Biotechnology & Bioengineering. 79 (2002) 53–73. [12] Varma A, Palsson B O. Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110..
Applied & Environmental Microbiology. 60 (1994) 3724–3731. [13] Luo, RY, Liao. Dynamic analysis of optimality in myocardial energy metabolism under normal and ischemic conditions. Molecular Systems Biology. 2 (2006) 2–2. [14] Noack R. D. Fell: Frontiers in Metabolism. Understanding the Control of Metabolism. XII and 301 pages, numerous figures and tables. Portland Press, London 1996. Price 18.95 05. Food. 41 (1997) 187–188. [15] Savageau M A, Voit E O, Irvine D H. Biochemical systems theory and metabolic control theory: 1. fundamental similarities and differences. Mathematical Biosciences. 86 (1987) 127–145. [16] Liu J Z, Weng L P, Zhang Q L, et al. A mathematical model for gluconic acid fermentation by Aspergillus niger. Biochemical Engineering Journal. 14 (2003) 137–141. [17] Bastin G., L. Chen, V. Chotteau, Can we Identify Biotechnological Processes ?, Proceedings of IFAC, Modelling and Control of Biotechnological Processes, Colorado, USA, 1992, pp. 83–88. [18] Ratkov A, Georgiev T, Kristeva J, et al. Modelling of L-valine fed-batch fermentation process. International Conference on Information Technology Interfaces. (2000) 397–402. [19] Georgiev T, Ratkov A, Kristeva J, et al. Improved Mathematical Model Of L-Lysine Fermentation Process Based On Manure. International Conference on Information Technology Interfaces. 1 (2002) 401–404. [20] Ratkov A, Georgiev T, Ivanova V, et al. Comparative studies of fed-batch
fermentation processes for production of L-lysine and L-valine based on mathematical models. International Conference on Information Technology Interfaces IEEE. (2003) 513–518. [21] Ratkov A, Georgiev T, Ivanova V, et al. Investigation of L-lysine fed-batch fermentation process with droppings by mathematical modeling. International Conference on Information Technology Interfaces IEEE. 1 (2004) 543–547. [22] Georgiev, Todorov T, Dimov K, et al. Modelling Of Repeated Fed-Batch Fermentation Process For L-Lysine Production. International Conference on Information Technology Interfaces IEEE. (2006) 525–530. [23] Georgiev T, Todorov K, Ratkov A. Mathematical Modeling of the Process for Microbial Production of Branched Chained Amino Acids. Bioautomation. 13 (2009). [24] Znad H, Markos J, Bales V. Production of gluconic acid from glucose by Aspergillusniger: growth and non-growth conditions. Process Biochemistry. 39 (2004) 1341–1345. [25] Godjevargova T, Dayal R, Turmanova S. Gluconic acid production in bioreactor with immobilized glucose oxidase plus catalase on polymer membrane adjacent to anion-exchange membrane. Macromolecular Bioscience. 4 (2004) 950–956. [26] Fan QQ, L ¨u ZM, Yan XF and Guo MJ, Chemical process dynamic optimization based on hybrid differential evolution algorithm integrated with Alopex. 20 (2013) 950–959.
S1369-703X(16)30150-4 http://dx.doi.org/doi:10.1016/j.bej.2016.05.009 BEJ 6476
To appear in:
Biochemical Engineering Journal
Received date: Revised date: Accepted date:
9-11-2015 17-5-2016 29-5-2016
Please cite this article as: Xinchao Wang, Xuefeng Yan, Fei Lu, Meijin Guo, Yingping Zhuang, Power series kinetic model based on generalized stoichiometric equations for microbial production of sodium gluconate, Biochemical Engineering Journal http://dx.doi.org/10.1016/j.bej.2016.05.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Power series kinetic model based on generalized stoichiometric equations for microbial production of sodium gluconate XinchaoWang,aXuefeng Yana*, FeiLub, MeijinGuob, YingpingZhuangb (a: Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology, Shanghai 200237, P. R. China b: State Key Laboratory of Bioreactor Engineering, East China University of Science and Technology, Shanghai 200237, P. R. China）
Corresponding author: Prof. Xuefeng Yan Email address: [email protected] Address: P.O. BOX 293, MeiLong Road 130, Shanghai, 200237, P. R. China Tel/Fax: +86-21-64251036
Highlights Power series kinetic model is developed for microbial production of sodium gluconate. The kinetic model is based on a generalized stoichiometric equations and a typical enzyme kinetic structure. The kinetic model can describe the fermentation process with sufficient accuracy. The kinetical model is simple.
Abstract Two main approaches are available for modeling of the fermentation process; these two are building an unstructured dynamic model and quantitative analysis of the metabolic network. The first one often employs several classic equations mostly derived from empirical knowledge and observation rather than mechanism knowledge. The second one is complicated because it requires sufficient biological information on cellular metabolic pathways. The objective of this article is to develop a kinetic model of the microbial production of sodium gluconate by using generalized stoichiometric equations and a typical enzyme kinetic structure called power series to overcome the shortcomings of previous methods.
The proposed kinetic model can describe the microbial growth of fungus as well as the interaction among dissolved oxygen, fungal metabolism, and product formation. Six batches were selected from seven batches of experimental sample data for modeling and analysis. The fitting precision was acceptable. The key parameters were analyzed based on the model. The main advantage of this model is that it has a simple structure based on the mechanism and can describe the fermentation process with sufficient accuracy. Keywords: fermentation; dynamic modeling; fungi; microbial growth; enzymes.
1. INTRODUCTION Sodium gluconate is an important material widely utilized as a firming,
stabilizing, or buffering agent in food, textile, pharmaceutical, and construction industries [1–3]. In recent years, it is also becoming a novel carbon source for fuels and chemicals production, such as ethanol production
[4-6]
. Many approaches for the
production of sodium gluconate are available, such as biochemical fermentation, electrochemical oxidation, homogeneous chemical oxidation and heterogeneous catalysis oxidation. At present, microbial production of sodium gluconate or fermentation by Aspergillus niger is the most preferred method [7–10]. The fermentation process can be modeled by two different models: structured models based on the analysis of metabolic pathways and unstructured models in which biomass is described by one variable. A structured model is difficult to build
[11]
because it requires sufficient
biological information on intracellular metabolic pathways. Two approaches can be applied to build a structured model. One involves establishing flow equilibrium equations based on the cellular metabolic network by using stoichiometric coefficients and selecting an objective for optimization
[12–13]
. The problem becomes a linear
optimization problem that fails to express many nonlinear features of the model. The other method involves kinetic analyses, such as enzyme kinetic analysis, metabolic control analysis
[14]
, and biochemical system theory [15].The problems include how to
guarantee feasibility, obtain sufficient constraints, and reduce computational difficulty. Unstructured models have simple forms. Previously proposed unstructured models can describe the fermentation process with satisfactory accuracy
[16]
. The
Monod equation and the logistic equation can be utilized to describe the growth trend of cells with different properties. The Luedeking–Piret and Luedeking–Piret/like equations can be used to describe production formation and glucose consumption. However, these classic equations are mostly derived from empirical knowledge and observation rather than mechanism knowledge. The proposed investigation approach attempts to combine structured and unstructured model features into a simple kinetic model that can describe the fermentation process with sufficient accuracy. Two main steps are required: describe the fermentation process through generalized stoichiometric equations and describe the relationship between reaction rate and metabolite concentration through the use of a power series structure. The parameters in the model can be categorized into two classes, namely, yield coefficients, which are determined by the structure of the generalized stoichiometric reactions, and kinetic rates, which are determined by specific metabolism pathways [17].
2. EXPERIMENTAL PROCEDURES 2.1 Microorganism The industrial strain for the production of sodium gluconate, Aspergillus niger (AN151) was supplied by Shan Dong Fuyang Biological Technology Co., Ltd.
2.2 Culture methods The A. niger strain was activated in a 250 mL flask (50 mL activation medium).
The activation medium slant inoculated with AN151 strain was incubated at 35 °C until it was covered with dense spores. The spores were harvested by washing the slant with 50 mL sterilized water. The formulation of the strain activation culture medium is 60.0 g/L glucose, 0.20 g/L urea, 0.13 g/L KH2PO4, 0.15 g/L MgSO4, 1.00 g/L corn steep liquor (Fu Yang Biology Co., Ltd., China), 5.00 g/L CaCO3, and 20.0 g/L agar. A total of 50 mL spore suspension was inoculated in a 15 L stirred bioreactor (9 L working volume) and cultivated for 18 h. Temperature and pressure were maintained at 38 °C and 0.1 MPa, respectively. The pH value was controlled at 5.5 by 7.5 M NaOH solution. Aeration and agitation rates were set to 0.8 vvm (air volume/culture volume/min) and 500 rpm, respectively. The formulation of the seed culture medium is 250 g/L glucose, 0.50 g/L KH2PO4, 1.80 g/L (NH4)2HPO4, 0.19 g/L MgSO4, 2.10 g/L corn steep liquor, and 0.20 mL/L polyether defoamer (Si Xin Scientific-Technological Application Research Institute Co., Ltd., Nanjing, China). A total of 4.5 L seeds were transferred into 50 L stirred bioreactor (30 L working volume). The pH, temperature, and pressure values during fermentation were similar to those during seed cultivation. Aeration and agitation rates were set to 1.2 vvm and 550 rpm, respectively. The fermentation ended when the glucose concentration was lower than 3 g/L. The formulation of the fermentation culture medium is 330 g/L glucose, 0.55 g/L KH2PO4, 0.40 g/L (NH4)2HPO4, 0.20 g/L MgSO4, and 0.20 mL/L polyether defoamer. All the culture media were sterilized at 115 °C for 20 min, and their initial pH
were adjusted to 7.0 by using 1 M NaOH solution, so that gluconic acid can turn into sodium gluconate.
2.3 Analytical methods Glucose concentration was measured with a hexokinase-glucose 6-phosphate dehydrogenase assay kit (Shanghai Ke Xin biotech Co., Ltd., China). Gluconic acid (GA) was quantitatively analyzed through high-performance liquid chromatography (HP 1100; Agilent) at 210 nm. AC18-H column (4.6 × 250 mm; Sepax) was utilized. The flow rate was set to1 mL/min. Elution was implemented with 3 M methanol solution and 0.25 M phosphate solution (1:1). The column temperature was maintained at 28 °C. Cell growth was monitored by measuring dry mycelia weight (DCW). A total of 50 ml fermentation broth was filtered through a filter membrane (0.45 µm). The cells were washed twice with distilled water, dried at 105 °C for 36 h, and equilibrated at room temperature in a desiccator. Dissolved oxygen was measured with Mettler electrode.
3. POWER SERIES KINETIC MODEL BASED ON GENERALIZED STOICHIOMETRIC
EQUATIONS
FOR
SODIUM
GLUCONATE
PRODUCTION To model the fermentation process, the following four main procedures need to be implemented [18–23].
(1) Determination of generalized stoichiometric reactions (2) Determination of the kinetic structure of the reaction rates (3) Establishment of dynamic models of the fermentation process (4) Determination of the model parameters
3.1 Hypothesis about generalized stoichiometric equations We assumed that three main generalized stoichiometric equations are involved in the fermentation process; these three are expressed as 𝑟1
S + X → X, 𝑟2
C + S + X → 𝐻2 𝑂 + 𝐶𝑂2,
(1)
𝑟3
C + S + X → P, Where 𝑟𝑖 stands for the rates of the generalized stoichiometric reactions; X denotes biomass concentration in g/L; S denotes substrate concentration, which stands for glucose, in g/L; P is a notation of produced sodium gluconate in g/L; and C denotes dissolved oxygen tension in %. In the equations, reaction 1 describes cell growth and can be regarded as a self-catalyzed reaction. Reaction 2 describes cell metabolism and is a full oxidation process. Reaction 3 describes product formation, in which oxygen, substrate, and enzyme are the three main reactants [24–25].
3.2 Hypothesis about models of reaction rates For each rate of the generalized stoichiometric reactions, a power series structure
was utilized as follows: 𝑟1 = 𝑆𝑘1 ∗ 𝑋𝑘2 , 𝑟2 = 𝑆𝑘3 ∗ 𝐶𝑘4 ∗ 𝑋𝑘5 ,
(2)
𝑟3 = 𝑆𝑘6 ∗ 𝐶𝑘7 ∗ 𝑋𝑘8 , Where 𝑘𝑖 denotes the parameters obtained by simulation and optimization that only depend on metabolic properties; 𝑟𝑖 denotes the rates of the generalized stoichiometric reactions.
3.3 State space equations Based on the previous assumption, the state space equations describing the kinetics of the fermentation process are as follows: d𝒁 dt dC dt
= 𝑲𝒓,
(3)
= 𝐶(𝑡),
Where 𝒁𝐓 = [𝑋, 𝑃, 𝑆]𝑇 is the state space vector, 𝑟 𝑇 = [𝑟1 , 𝑟2 , 𝑟3 ]𝑇 is the vector of kinetic rates, t is time, and 𝑲 is the matrix of yield coefficients. 𝑘9 𝑲=[ 0 −𝑘13
−𝑘10 0 −𝑘14
−𝑘11 𝑘12 ] −𝑘15
(4)
In reactions 2 and 3, X only stands for enzymes produced by cells, so modification can be obtained as 𝑘10 = 𝑘11 = 0. For
dC dt
, the situation is rather complicated. Hence, we used a quadratic curve
fitting of t to describe the oxygen change rate temporarily. And for 𝐶(𝑡), it was obtained in each batch.
3.4 Optimization After establishing the state space equations, the model parameters were obtained through nonlinear optimization. To achieve high accuracy, relative error was selected as the optimization objective. Min = ∑3𝑖=1 𝑅𝐸𝑖 ,
(5)
𝑦𝑖_𝑝𝑟𝑒𝑑 −𝑦𝑖_𝑒𝑥𝑝
1
𝑅𝐸𝑖 = 𝑛 ∑𝑛𝑗=1 |
𝑦𝑖_𝑒𝑥𝑝
|,
Where n stand for the total amount of sample data, 𝑦𝑖_𝑝𝑟𝑒𝑑 and 𝑦𝑖_𝑒𝑥𝑝 stand for the predicted value and experimental data of the ith state variable respectively. The optimization problem was solved with the modified DE algorithm Alopex-DE[26]. Detailed information on this modified algorithm is available elsewhere and will not be discussed further in this paper.
4. RESULTS AND DISCUSSION 4.1 General performance To analyze the accuracy of the kinetic model, several evaluation indices were adopted. We selected root mean squared error (RMSE) and relative error (RE) as the evaluation indices. 2 ∑𝑛 𝑖=1(𝑦𝑝𝑟𝑒𝑑 −𝑦𝑒𝑥𝑝 )
RMSE = √ 1
𝑛 𝑦𝑝𝑟𝑒𝑑 −𝑦𝑒𝑥𝑝
RE = 𝑛 ∑𝑛𝑖=1 |
𝑦𝑒𝑥𝑝
|
(6)
Figure 1. Fitting results for batch 1.
Figure 2. Fitting results for batch 2.
Figure 3. Fitting results for batch 3. Figs 1 to 3 show the fitting results for each batch. We can see that the model is roughly in line with the experimental data, and the RMSE and RE of the model for each variable in three batches are shown in Tables 1 and 2. Table 1.RMSE of the model for each variable in three batches Fermentation batches
X
P
S
C
Batch 1
0.006
0.9367
0.5696
3.9198
Batch 2
0.0109
0.8227
0.5775
2.6368
Batch 3
0.0197
1.3609
0.8085
2.7704
Table 2.RE of the model for each variable in three batches Fermentation batches
X
P
S
C
Batch 1
0.0603
0.0841
0.048
0.0477
Batch 2
0.1021
0.0623
0.0345
0.0273
Batch 3
0.0692
0.0291
0.0523
0.0337
The parameters were obtained for the model as below. Batch 1 to 3 use the same set of parameters. Table 3. Parameters of the model 𝑘1
𝑘2
𝑘3
𝑘4
𝑘5
𝑘6
𝑘7
1.7406
0.8512
0.5137
0.494
1.2494
-0.1141
0.3359
𝑘8
𝑘9
𝑘12
𝑘13
𝑘14
𝑘15
0.4196
0.0003
1.4391
0.0209
-0.0801
1.1568
4.2 Microbial growth The cells in the fermentation process exhibited a typical growth trend. The cells entered the exponential growth phase, which lasted for more than 10 h, and then the stationary phase. The strain began to produce sodium gluconate as soon as the cells entered the exponential phase. Because even the strain was at a low density, the enzyme produced by the strain, such as glucose oxidase and lactonase, can still be sufficient for glucose use in product formation when there exits sufficient dissolved oxygen. The initial trend of cell growth was similar to that of sodium gluconate production.
4.3 Product formation The results also reveal that sodium gluconate is not related to cell growth in the stationary phase. In this phase, the enzyme for product formation produced by the strain changed slightly, so the constraints probably transferred from enzyme to
substrate concentration and oxygen concentration.
4.4 Substrate and oxygen uptakes Substrate uptake is related to oxygen uptake. Based on the generalized stoichiometric equations established previously, this phenomenon is reasonable. In particular, when cells entered the stationary phase, the activity of reaction 1 is low, so substrate and oxygen uptakes seemed more related.
5. ANALYSIS OF THE KEY PARAMETER WITH THE MODEL Some important factors were found during the optimization of the fermentation techniques. Dissolved oxygen is one of them, so we consider that it is a key parameter on the fermentation process. To analyze it, the determined model was utilized to predict the value of three state variables (biomass, glucose, sodium gluconate) under a different condition. The fermentation techniques of batch 4 to 6 are a lot different from that of batch 1 to 3. So it was selected that the model whose parameters were determined by optimization with experimental data from batch 4 and used the experimental data of initial time from batch 5 and 6 for prediction.
Figure 4. Prediction results under the condition of low dissolved oxygen for batch 5.
Figure 5.Prediction results under the condition of low dissolved oxygen for batch 6.
According to Figs 4 and 5, it can be seen that when the dissolved oxygen is not controlled at the same level as the batches before, the results are also different from the ones before. In these two batches, the dissolved oxygen is controlled at a low level by mainly changing the air inflow and agitation rate. As the experimental results are shown, when dissolved oxygen declines rapidly, product formation deteriorates, glucose uptake remains similar, and mycelium also drops. The prediction made by the model is quite well. In this way, the experimental results and the model both indicate that the dissolved oxygen is both important to microbial use and product formation use, and also prove that dissolved oxygen is a key parameter in the fermentation
process for sodium gluconate.
6. CONCLUSIONS A power series kinetic model based on generalized stoichiometric equations for microbial production of sodium gluconate was developed. Compared with unstructured dynamic models with several classic mechanism equations, the proposed model can better describe the growth of fungus and the interaction among dissolved oxygen, fungal metabolism, and product formation. Compared with structured models based on the analysis of metabolic pathways, the proposed model is easier to build, and the three generalized stoichiometric equations describe the substrate uptake of different uses separately, which reflects the intracellular metabolic pathways clearly. Each generalized stoichiometric equation used is based on the power series, which divides the model parameters into two types. Thus, the model combines known biological mechanism with simplicity. The fitting precision of the model is acceptable.
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