Application of mathematical models to the determination optimal glucose concentration and light intensity for mixotrophic culture of Spirulina platensis

The effects of initial glucose concentration and light intensity on specific growth rate, phycocyanin concentration and cell dry weight concentration in mixotrophic batch cultivation of Spirulina platensis using both shake flask and fermenter were investigated. Based on experimental results in shake flask culture, a number of mathematical models were constructed, and the optimal initial glucose concentration and the optimal light intensity were calculated to be S_opt=2.4471 g liter⁻¹ and L_opt=3.8632 klx. Finally, a time-dependent kinetic model for mixotrophic batch cultivation of Spirulina platensis in fermenter was also proposed. This was in good agreement with the experimental results and could be employed to predict the production of biomass and phycocyanin, and the consumption of glucose in fermenter culture.     

Impact of initial conditions on extant microbial kinetic parameter estimates: application to chlorinated ethene dehalorespiration

Monod kinetics are the foundation of mathematical models of many environmentally important biological processes, including the dehalorespiration of chlorinated ethene groundwater contaminants. The Monod parameters—q _max, the maximum specific substrate utilization rate, and K _S, the half-saturation constant—are typically estimated in batch assays, which are superficially simple to prepare and maintain. However, if initial conditions in batch assays are not chosen carefully, it is unlikely that the estimated parameter values will be meaningful because they do not reflect microbial activity in the environmental system of interest, and/or they are not mathematically identifiable. The estimation of q _max and K _S values that are highly correlated undoubtedly contributes significantly to the wide range in reported parameter values and may undermine efforts to use mathematical models to demonstrate the occurrence of natural attenuation or predict the performance of engineered bioremediation approaches. In this study, a series of experimental and theoretical batch kinetic assays were conducted using the tetrachloroethene-respirer Desulfuromonas michiganensis to systematically evaluate the effects of initial batch assay conditions, expressed as the initial substrate (S ₀)-to-initial biomass concentration (X ₀) ratio (S ₀/X ₀) and the S ₀/K _S ratio on parameter correlation. An iterative approach to obtain meaningful Monod parameter estimates was developed and validated using three different strains and can be broadly applied to a range of other substrates and populations. While the S ₀/X ₀ ratio is critical to obtaining kinetic parameter estimates that reflect in situ microbial activity, this study shows that optimization of the S ₀/K _S ratio is key to minimizing Monod parameter correlation.     

Optimization of Culture Conditions for Fermentation of Soymilk Using Lactobacillus casei by Response Surface Methodology

Soymilk was fermented with Lactobacillus casei, and statistical experimental design was used to investigate factors affecting viable cells of L. casei, including temperature, glucose, niacin, riboflavin, pyridoxine, folic acid and pantothenic acid. Initial screening by Plackett-Burman design revealed that among these factors, temperature, glucose and niacin have significant effects on the growth of L. casei. Further optimization with Box-Behnken design and response surface analysis showed that a second-order polynomial model fits the experimental data appropriately. The optimum conditions for temperature, glucose and niacin were found to be 15.77 °C, 5.23 and 0.63 g/L, respectively. The concentration of viable L. casei cells under these conditions was 8.23 log₁₀ (CFU/mL). The perfect agreement between the observed values and the values predicted by the equation confirms the statistical significance of the model and the model’s adequate precision in predicting optimum conditions.     

Fed-batch sorbitol to sorbose fermentation by A. suboxydans

Batch kinetics for sorbitol to sorbose bioconversion was studied at 20% sorbitol concentration. The culture featured 90% conversion of sorbitol to sorbose in 20 hours. Increasing the initial substrate concentration in the bioreactor decreased the culture specific growth rate. At 40% initial sorbitol concentration no culture growth was observed. The batch kinetics and substrate inhibition studies were used to develop the Mathematical Model of the system. The model parameters were identified using the original batch kinetic data (S _o =20%). The developed mathematical model was adopted to fed-batch cultivation with the exponential nutrient feeding. The fed-batch model was simulated and implemented experimentally. No substrate inhibition was observed in the fed-batch mode and it provided an overall productivity of 12.6?g/l-h. The fed-batch model suitably described the experimentally observed results. The model is ready for further optimization studies.     

Production of a highly glucose tolerant β-glucosidase by Paecilomyces variotii MG3: optimization of fermentation conditions using Plackett–Burman and Box–Behnken experimental designs

β-Glucosidases (β-d-glucoside glucohydrolase, 3.2.1.21) are a group of enzymes mainly involved in the hydrolysis of β-glycosidic bonds connecting carbohydrate residues in different classes of β-d glycosides. During cellulose degradation they convert cellobiose and cellooligosaccharides produced by the endo and exoglucanases to glucose. Most of the microbial β-glucosidases are inhibited by glucose. This limits their application in commercial scale cellulose degradation ventures. Solid state fermentation production of a highly glucose tolerant β-glucosidase by a novel isolate of Paecilomyces was optimized using a two step statistical experiment design. In the first step which employed a Plackett–Burman design, the effects of parameters such as moisture, temperature, pH, inoculum concentration, incubation time and different concentrations of (NH₄)₂SO₄, KH₂PO₄, NaCl, peptone and cellobiose were evaluated. The parameters with significant influence on the process were selected and fine tuned in the second step using a Box–Behnken design. The model obtained was validated and a peptone concentration of 2 g/l, inoculum concentration of 1.2 × 10⁶ spores/ml and an incubation period of 96 h were found to be optimum for the maximum production of the enzyme. The optimization resulted in a doubling of the enzyme production by the fungus.     

Statistical optimization of glucose oxidase production from Aspergillus niger NRC9 under submerged fermentation using response surface methodology

Response surface methodology (RSM), employing the fractional factorial design (FFD) was used to optimize the fermentation medium for the production of glucose oxidase (GOD) from a marine isolate (NRC9) of Aspergillus niger under submerged fermentation. The design was employed by selecting glucose, CaCO_3, ammonium phosphate and MgSO₄ concentrations as model factors by ‘one variable at a time’ experiment. A second-order quadratic model and response surface method showed that the optimum concentrations (g/l) glucose, 100; CaCO₃, 25; (NH₄)₂HPO₄, 1.8 and 0.4 of MgSO₄, resulted in an improvement of GOD production (170?±?0.88 U/ml) as compared to the initial level (109.81?±?1.38 U/ml) after four days of incubation at 200 rpm and 30 °C, whereas its predicted value obtained by the quadratic model was 164.36 U/ml. Analysis of variance (ANOVA) showed a high coefficient of determination value (R ²) of 0.967, ensuring a satisfactory adjustment of the quadratic model with the experimental data. This is the first report on production of glucose oxidase from a marine fungal isolate, Aspergillus niger NRC9, using statistical experimental design and response surface methodology in optimization of its production under submerged fermentation.     

Growth kinetics of EDTA biodegradation by Burkholderia cepacia

A pure culture of an EDTA-degrading strain was isolated from the Taiwan environment. It was identified as Burkholderia cepacia, an aerobic bacterium, elliptically shaped with a length of 5–15 m. The degradation assay showed that the degradation efficiency of Fe-EDTA by B. cepacia was approximately 91%. Evaluation of kinetic parameters showed that Fe-EDTA degradation followed substrate inhibition kinetics. This is evident from the decrease in specific growth rate with an increase in the initial substrate concentration greater than 500 mg/l. To estimate the kinetic parameters – _max, K_S and K_I, five substrate–inhibition models were used. From the results of non-linear regression, the value of _max ranged from 0.150 to 0.206 d^–1, K_S from 74 to 87 mg/l, and K_I from 890 to 2289 mg/l. The five models were found to underestimate the maximum specific growth rate by 1.5–3.7. Therefore, predictions based on these models would result in lower predicted value than those from the experimental kinetic data.     

An unstructured kinetic model to study NaCl effect on volatile ester fermentation by <Emphasis Type="Italic">Candida etchellsii</Emphasis> for soy sauce production

Salt-tolerant aromatic yeast is an important microorganism arising from the solid state fermentation of soy sauce. The fermentation kinetics of volatile esters by Candida etchellsii was studied in a batch system. The data obtained from the fermentation were used for determining the kinetic parameters of the model. Batch experimental results at four NaCl levels (180, 200, 220, and 240 g/L) were used to formulate the parameter estimation model. The kinetic parameters of the model were optimized by specifically designed Runge-Kutta Genetic Algorithms (GA). The resulting mathematical model for volatile ester production, cell growth and glucose consumption simulates the experimental data well. The resulting new model was capable of explaining the behavior of volatile ester fermentation. The optimized parameters (μ_o, X _max, K _i, α, β, Y _X/S, m, and Y _P/S) were characterized by a correlation of functions assuming salinity dependence. The kinetic models optimized by GA describe the batch fermentation process adequately, as demonstrated by our experimental results.     

β-Mannanase production and kinetic modeling from carob extract by using recombinant Aspergillus sojae

The main objectives of this study were to optimize β-mannanase fermentation conditions by using Response Surface Methodology (RSM) and to model kinetically using the kinetic models. Based on the results, the optimum fermentation conditions were found to be initial sugar concentration of 10°Bx, whey concentration of 0.75% [w/v], and inoculum size of 8% (v/v). Under optimized conditions, β-mannanase activity (P), sugar consumed (ΔS), maximum β-mannanase production rate (Q_P), and sugar utilization yield (SUY) were 687.89 U/mL, 47.38 g/L, 118.54 U mL^–1 day^–1, and 69.73%, respectively. Kinetic models were employed to describe the optimum β-mannanase fermentation process. The kinetic analysis of β-mannanase fermentation showed that β-mannanase fermentation is growth associated because the α value (U/mgX) is approximately 330-fold higher than the β value (U/mgX·hr). Nevertheless, maintenance value (Z) was lower than γ value, thus showing that Aspergillus niger mainly utilizes the sugars for β-mannanase production and fungal growth. Consequently, carob extract and whey powder could be used to be cost-effective carbon and organic nitrogen sources, respectively. It was clearly indicated that the suggested kinetic models can successfully describe the fungal growth, β-mannanase production, and substrate consumption.     

In Vitro Kinetic Analysis of Oligofructose Consumption by Bacteroides and Bifidobacterium spp. Indicates Different Degradation Mechanisms

The growth of pure cultures of Bacteroides thetaiotaomicron LMG 11262 and Bacteroides fragilis LMG 10263 on fructose and oligofructose was examined and compared to that of Bifidobacterium longum BB536 through in vitro laboratory fermentations. Gas chromatography (GC) analysis was used to determine the different fractions of oligofructose and their degradation during the fermentation process. Both B. thetaiotaomicron LMG 11262 and B. fragilis LMG 10263 were able to grow on oligofructose as fast as on fructose, succinic acid being the major metabolite produced by both strains. B. longum BB536 grew slower on oligofructose than on fructose. Acetic acid and lactic acid were the main metabolites produced when fructose was used as the sole energy source. Increased amounts of formic acid and ethanol were produced when oligofructose was used as an energy source at the cost of lactic acid. Detailed kinetic analysis revealed a preferential metabolism of the short oligofructose fractions (e.g., F₂ and F₃) for B. longum BB536. After depletion of the short fractions, the larger oligofructose fractions (e.g., F₄, GF₄, F₅, GF₅, and F₆) were metabolized, too. Both Bacteroides strains did not display such a preferential metabolism and degraded all oligofructose fractions simultaneously, transiently increasing the fructose concentration in the medium. This suggests a different mechanism for oligofructose breakdown between the strain of Bifidobacterium and both strains of Bacteroides, which helps to explain the bifidogenic nature of inulin-type fructans.     

Der Einfluß der Prozeßparameter auf die Ethanolausbeute in Batchprozessen bei Verwendung von Saccharomyces cerevisiae

The production costs of ethanol are dependent on the efficiency of the substrate-ethanol conversion to a high degree. The more the substrate used during the fermentation is converted into alcohol the better is the economy of the process. Therefore the ethanol yield Y _S^P is an important object of the process optimization. In batch fermentation processes the most essential influence factors are the initial biomass concentration X₀, the initial substrate concentration S₀, the temperature T, and the pH-value. A model reflecting the complex relationships between these influence factors and the ethanol yield could be obtained by regression. It allows an exact valuation of these optimum process parameters which are necessary for realizing high ethanol yields in the batch fermentation. For the strain Saccharomyces cerevisiae Sc 5 used in this research was found an ethanol yield maximum Y_S^P = 0˙5384 at the parameters X₀ = 64.61 g/l S₀ = 82.91 g/l T = 36.45°C pH = 6.54.     

Kinetics of phenol degradation using Pseudomonas putida MTCC 1194

Pseudomonas putida (MTCC 1194) has been used to degrade phenol in water in the concentration range 100–1000?ppm. The inhibition effects of phenol as substrate have become predominant above the concentration of 500?ppm (5.31?mmoles/dm³). The optimum temperature and initial pH required for maximum phenol biodegradation were 30?°C and 7.00 respectively. From the degradation data the activation energy (E _a ) was found to be equal to 13.8?kcal/g mole substrate reacted. The most suitable inoculum age and volume for highest phenol degradation were 12?hrs and 7% v/v respectively. Surfactants had negligible effect on phenol biodegradation process for this microorganism. Monod model has been used to interpret the free cell data on phenol biodegradation. The kinetic parameters have been estimated upto initial concentration of 5.31?mmoles/dm³. μ _max and K _S gradually increased with higher concentration of phenol. However, beyond the phenol concentration of 5.31?mmoles/dm³, the inhibition became prominant. The μ _max has been to be a strong function of initial phenol concentration. The simulated and the experimental phenol degradation profiles have good correspondence with each other.     

Kinetic modeling of <Emphasis Type="Italic">Moorella thermoacetica</Emphasis> growth on single and dual-substrate systems

Acetic acid is an important chemical raw material that can be produced directly from sugars in lignocellulosic biomass. Development of kinetic models that capture the bioconversion dynamics of multiple sugar systems will be critical to optimization and process control in future lignocellulosic biorefinery processes. In this work, a kinetic model was developed for the single- and dual-substrate conversion of xylose and glucose to acetic acid using the acetogen Moorella thermoacetica. Batch fermentations were performed experimentally at 20 g L^?1 total sugar concentration using synthetic glucose, xylose, and a mixture of glucose and xylose at a 1:1 ratio. The product yield, calculated as total product formed divided by total sugars consumed, was 79.2, 69.9, and 69.7 % for conversion of glucose, xylose, and a mixture of glucose and xylose (1:1 ratio), respectively. During dual-substrate fermentation, M. thermoacetica demonstrated diauxic growth where xylose (the preferred substrate) was almost entirely consumed before consumption of glucose began. Kinetic parameters were similar for the single-substrate fermentations, and a strong linear correlation was determined between the maximum specific growth rate μ _max and substrate inhibition constant, K _s . Parameters estimated for the dual-substrate system demonstrated changes in the specific growth rate of both xylose and glucose consumption. In particular, the maximum growth rate related to glucose tripled compared to the single-substrate system. Kinetic growth is affected when multiple substrates are present in a fermentation system, and models should be developed to reflect these features.     

Optimization of Biomass Conversion to Levulinic Acid in Acidic Ionic Liquid and Upgrading of Levulinic Acid to Ethyl Levulinate

Levulinic acid (LA) is a versatile platform chemical that can be derived from biomass as an alternative to fossil fuel resources. Herein, the optimization of LA production from glucose and oil palm fronds (OPF) catalyzed by an acidic ionic liquid; 1-sulfonic acid-3-methyl imidazolium tetrachloroferrate ([SMIM][FeCl₄]) have been investigated. Response surface methodology based on Box-Behnken design was employed to optimize the LA yield and to examine the effect and interaction of reaction parameters on the LA production. The reaction parameters include reaction temperature, reaction time, feedstock loading, and catalyst loading. From the optimization study, the predicted mathematical models for LA production from glucose and OPF covered more than 90 % of the variability in the experimental data. At optimum conditions, 69.2 % of LA yield was obtained from glucose, while 24.8 % of LA yield was attained from OPF and registered 77.3 % of process efficiency. The recycled [SMIM][FeCl₄] gave sufficient performance for five successive cycles. Furthermore, the optimum LA produced from glucose and OPF can be directly converted to ethyl levulinate through esterification over the [SMIM][FeCl₄] catalyst. This study highlights the potential of [SMIM][FeCl₄] for biorefinery processing of renewable feedstocks at mild process conditions.     

Simultaneous versus sequential optimal experiment design for the identification of multi-parameter microbial growth kinetics as a function of temperature

Optimal experiment design for parameter estimation (OED/PE) has become a popular tool for efficient and accurate estimation of kinetic model parameters. When the kinetic model under study encloses multiple parameters, different optimization strategies can be constructed. The most straightforward approach is to estimate all parameters simultaneously from one optimal experiment (single OED/PE strategy). However, due to the complexity of the optimization problem or the stringent limitations on the system's dynamics, the experimental information can be limited and parameter estimation convergence problems can arise. As an alternative, we propose to reduce the optimization problem to a series of two-parameter estimation problems, i.e., an optimal experiment is designed for a combination of two parameters while presuming the other parameters known. Two different approaches can be followed: (i) all two-parameter optimal experiments are designed based on identical initial parameter estimates and parameters are estimated simultaneously from all resulting experimental data (global OED/PE strategy), and (ii) optimal experiments are calculated and implemented sequentially whereby the parameter values are updated intermediately (sequential OED/PE strategy).This work exploits OED/PE for the identification of the Cardinal Temperature Model with Inflection (CTMI) (Rosso et al., 1993). This kinetic model describes the effect of temperature on the microbial growth rate and encloses four parameters. The three OED/PE strategies are considered and the impact of the OED/PE design strategy on the accuracy of the CTMI parameter estimation is evaluated. Based on a simulation study, it is observed that the parameter values derived from the sequential approach deviate more from the true parameters than the single and global strategy estimates. The single and global OED/PE strategies are further compared based on experimental data obtained from design implementation in a bioreactor. Comparable estimates are obtained, but global OED/PE estimates are, in general, more accurate and reliable.     

Biosorption of uranium by magnetically modified Rhodotorula glutinis

Adsorption of uranium from aqueous solution onto the magnetically modified yeast cell, Rhodotorula glutinis, was investigated in a batch system. Factors influencing sorption such as initial solution pH, biomass dosage, contact time, temperature, initial uranium concentration and other common cations were analyzed. Sorption isotherm, kinetic and thermodynamic studies of uranium on magnetically modified R. glutinis were also carried out. The temperature dependent equilibrium data agreed well with the Langmuir model. Kinetic data obtained at different temperatures were simulated using pseudo-first-order and pseudo-second-order kinetic models, the pseudo-second-order kinetic model was found to describe the data better with correlation coefficients near 1.0. The thermodynamic parameters, ΔH°, ΔS° and ΔG° were calculated from the sorption data gained at different temperatures. These thermodynamic parameters showed that the sorption process was endothermic and spontaneous. All results indicated that magnetically modified R. glutinis can be a potential sorbent for uranium wastewater treatment.     

Kinetics of potato starch fermentation by Schwanniomyces castellii

The growth behaviour of Schwanniomyces castellii in slurry fermentation systems using untreated potato starch as substrate was studied in order to asses the eventual effect of the initial concentration of substrate (S_o) on cell growth rate. By applying the elementary balance method in combination with a Monod-type kinetic equation it was possible to formulate not only an unstructured model, but also the stoichiometry for such a yeast fermentation process. From a kinetic viewpoint, the Monod model was found to be redundant with respect to the pseudo-first order one, it being impossible to discriminate the contribution of v _M and K _S on the overall fermentation kinetics. Whereas the main yield coefficients appeared to be independent of S _O, the pseudo-first order rate constant was found to be inversely proportional to S _O. Therefore, cell growth appears to be controlled by the initial amount of amylolytic enzymes, that is to some extent proportional to the inoculum size, instead of the initial concentration of potato starch, at least within the experimental range of 3 to 30 g dm³.     

Biosorption of Nickel(II) from aqueous solution by the fungal mat of Trametes versicolor (rainbow) biomass: equilibrium, kinetics, and thermodynamic studies

This study investigates the equilibrium, kinetics and thermodynamics of Nickel(II) biosorption from aqueous solution by the fungal mat of Trametes versicolor (rainbow) biomass. The optimum biosorption conditions like pH, contact time, biomass dosage, initial metal ion concentration and temperaturewere determined in the batch method. The biosorbent was characterized by FTIR, SEM and BET surface area analysis. The experimental data were analyzed in terms of pseudo-first-order, pseudo-secondorder and intraparticle diffusion kinetic models, further it was observed that the biosorption process of Ni(II) ions closely followed pseudo-second-order kinetics. The equilibrium data of Ni(II) ions at 303, 313, and 323 K were fitted to the Langmuir and Freundlich isotherm models. Langmuir isotherm provided a better fit to the equilibrium data andthe maximum monolayer biosorption capacity of the T. versicolor(rainbow) biomass for Ni(II) was 212.5 mg/g at pH 4.0. The calculated thermodynamic parameters, ΔG^○, ΔH^○, and ΔS^○, demonstrated that the biosorption of Ni(II) ions onto the T. versicolor (rainbow) biomass was feasible, spontaneous and endothermic at 303 ～ 323 K. The performance of the proposed fungal biosorbent was also compared with that of many other reported sorbents for Nickel(II) removal and it was observed that the proposed biosorbent is effective in terms of its high sorption capacity.     

Optimization of the growth parameters of Aspergillus foetidus

The batch production of gluconic acid in the presence of glucose, sucrose and molasses was investigated using free mycelia of Aspergillus foetidus NRRL 337 in shake flasks. Eight growth parameters were chosen as independent variables. The temperature, pH, substrate type and initial concentrations, inoculum percentage and shake rate directly affected the specific microorganism growth and gluconic acid production rates. The optimum temperature and initial pH values were found to be 33°C and five to six, respectively. The maximum specific growth and gluconic acid production rates were established as 57 g/dm³ of glucose, 75 g/dm³ of sucrose and 150 g/dm³ of molasses. The optimum values of the shake rate, inoculum percentage and initial ammonium nitrate concentration were determined as 100 1/min, 0.5% and 1.5 g/dm³, respectively. The maximum gluconic acid concentrations corresponding to these initial substrate concentrations were observed to be 8.3 g/dm³, 17.4 g/dm³ 37.0 g/dm³, respectively. The optimum specific microbial growth and gluconic acid production rates were found as 0.0145 1/h and 0.0375 g/g × h, respectively, for the fermentation conditions of S_Go = 57 g/dm³, T = 28°C, initial pH = 6.5, N = 84 1/min, A = 0.5 g/dm³ and I = 0.5%.