Modeling of batch fermentation kinetics for succinic acid production by Mannheimia succiniciproducens

Kinetic models are proposed for the batch production of succinic acid from glucose by Mannheimia succiniciproducens MBEL55E. The models include terms accounting for both substrate and product inhibitions. Experimental data collected from a series of batch fermentations with different initial glucose concentrations were used to estimate parameters and also to validate the models proposed. The optimal values of the parameters were approximated by minimizing the discrepancy between the model predictions and corresponding experimental data. The growth of M. succiniciproducens could be expressed by a modified Monod model incorporating inhibitions of glucose and organic acids accumulated in the culture broth. The Luedeking–Piret model was able to describe the formation of organic acids as the fermentation proceeded, in which succinic, acetic, and formic acids followed a mixed-growth-associated pattern. However, unexpectedly, lactic acid fermentation by M. succiniciproducens was nearly nongrowth-associated. In all cases, the model simulation matched well with the experimental observations, which made it possible to elucidate the fermentation characteristics of M. succiniciproducens during efficient succinic acid production from glucose. These models thus can be employed for the development and optimization of biobased succinic acid production processes.     

基于遗传算法的谷氨酸发酵动力学参数估计

把遗传算法应用于求解谷氨酸分批发酵动力学模型参数,取交叉概率Pc=0．8、变异概率Pm=0．06、初始种群为20、遗传世代数为200代,能进一步提高谷氨酸分批发酵过程状态变量的计算值与实验值的吻合程度。模拟值与实验值对比显示,该动力学模型能很好地反映谷氨酸分批发酵过程。     

红豆杉细胞悬浮培养结构化数学模型的探讨

用１０Ｌ机械搅拌式生物反应器悬浮培养红豆杉细胞,得到细胞生长、基质消耗和紫杉醇合成动力学曲线。经过代谢动力学分析建立了结构化数学模型。并将模型值与实验值进行比较,结果表明模型预测值与实验值较吻合。     

Modelling of simultaneous production of polygalacturonase and exopolysaccharide by Aureobasidium pullulans ATHUM 2915

The polymorphic fungus Aureobasidium pullulans ATHUM 2915, produced significant quantities of extracellular polygalacturonase and polysaccharide when grown, under controlled conditions, in liquid medium with pectin and glucose as carbon sources and nitrogen source as limited factor. Growth, substrate consumption and products formation were simulated by a structured mathematical model, which was compared with the experimental data from batch culture in a chemostat. This model was applied successfully in the study of some essential parameters influenced the process at various pH values.     

Robust parameter estimation during logistic modeling of batch and fed‐batch culture kinetics

Methods for robust logistic modeling of batch and fed‐batch mammalian cell cultures are presented in this study. Linearized forms of the logistic growth, logistic decline, and generalized logistic equation were derived to obtain initial estimates of the parameters by linear least squares. These initial estimates facilitated subsequent determination of refined values by nonlinear optimization using three different algorithms. Data from BHK, CHO, and hybridoma cells in batch or fed‐batch cultures at volumes ranging from 100 mL–300 L were tested with the above approach and solution convergence was obtained for all three nonlinear optimization approaches for all data sets. This result, despite the sensitivity of logistic equations to parameter variation because of their exponential nature, demonstrated that robust estimation of logistic parameters was possible by this combination of linearization followed by nonlinear optimization. The approach is relatively simple and can be implemented in a spreadsheet to robustly model mammalian cell culture batch or fed‐batch data. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Numerical modeling of ferrous-ion oxidation rate in Acidithiobacillus ferrooxidans ATCC 23270: optimization of culture conditions through statistically designed experiments

Statistically designed experimental strategy has been performed in order to evaluate and optimize nutritional and environmental parameters that affect ferrous ion oxidation rate in Acidithiobacillus ferrooxidans ATCC 23270. Plackett-Burman design was carried out to evaluate efficiently the biological significance of 10 culture conditions influencing ferrous-ion oxidation rate of A. ferrooxidans grown for 5 days in shake-flask batch mode on the newly modified 9-K media. Among ten fermentation factors examined, the most significant variables influencing ferrous-ion oxidation rate were statistically elucidated to be pH and calcium nitrate as positive contributors, whereas trace metals solution and potassium chloride were the most significant negative contributors. The optimal levels of the most significant three nutritional factors were further predicted from a polynomial model created from the data obtained from three level factorial design, a Box-Behnken design. Predicted optimal ferrous-ion oxidation rate Q(Fe2+) was recorded to be 0.148 (g Fe2+/l/hr). On verifying the predicted value, an experiment was performed under optimal predicted conditions and showed an actual experimental Q(Fe2+) of 0.152 g/l/hr, which was 2.7% over the predicted value. Our optimized medium formula gave overall five folds increase in ferrous-ion oxidation rates over the previously published data of standard 9-K medium on batch culture of A. ferrooxidans ATCC 23270 with higher mu(max) (hr(-1)) of 0.177 which was achieved within 75 h incubation in shake-flask culture.     

Development of a phenomenological modeling approach for prediction of growth and xanthan gum production using Xanthomonas campestris

An unstructured kinetic model for xanthan production is described and fitted to experimental data obtained in a stirred batch reactor. The culture medium was composed of several nitrogen sources (soybean hydrolysates, ammonium and nitrate salts) consumed sequentially. The model proposed is able to describe this sequential consumption of nitrogen sources, the consumption of inorganic phosphate and carbon, the evolution of biomass, and production of xanthan. The parameter estimation has been performed by fitting the kinetic model in differential form to experimental data. Runs of the model for simulating xanthan gum production as a function of the initial concentration of inorganic phosphate have shown the positive effect of phosphate limitation on xanthan yield, though diminishing rates of production. The model was used to predict the kinetic parameters for a medium containing a 2-fold lower initial phosphate concentration. When tested experimentally, the measured fermentation parameters were in close agreement with the predicted model values, demonstrating the validity of the model.     

Computer programs for modeling mammalian cell batch and fed-batch cultures using logistic equations

A MATLAB^® toolbox was developed for applying the logistic modeling approach to mammalian cell batch and fed-batch cultures. The programs in the toolbox encompass sensitivity analyses and simulations of the logistic equations in addition to cell specific rate estimation. The toolbox was first used to generate time courses of the sensitivity equations for characterizing the relationship between the logistic variable and the model parameters. Subsequently, the toolbox was used to describe CHO cell data from batch and fed-batch mammalian cell cultures. Cell density, product, glucose, lactate, glutamine, and ammonia data were analyzed for the batch culture while fed-batch analysis included cell density and product concentration. In all instances, experimental data were well described by the logistic equations and the resulting specific rate profiles were representative of the underlying cell physiology. The 6-variable batch culture data set was also used to compare the logistic specific rates with those from polynomial fitting and discrete derivative methods. The polynomial specific rates grossly misrepresented cell behavior in the initial and final stages of culture while those based on discrete derivatives had high variability due to computational artifacts. The utility of logistic specific rates to guide process development activities was demonstrated using specific protein productivity versus growth rate trajectories for the 3 cultures examined in this study. Overall, the computer programs developed in this study enable rapid and robust analysis of data from mammalian cell batch and fed-batch cultures which can help process development and metabolic flux estimation.     

Optimal design for the maximization of Penicillium cyclopium lipase production

Penicillium cyclopium triacylglycerol lipase production was maximized in stationary batch culture. We used a surface response methodology based on a Doehlert experimental design to study the effect on the lipase activity released in the culture medium of the three most important factors: substrate concentration, pH and inoculum. Besides reducing the number of experiments required for optimization, this technique allowed us to quantify the lipase activity in any part of the experimental domain.We determined an optimal set of conditions for high lipase production: 1% substrate (corn steep), pH 5.5 and an inoculum of 10(4) spores/ml. Between conditions giving the minimum and the maximum lipase production, we observed a nine-fold increase of both the predicted and measured values.     

Mathematical model of a batch acetone-butanol fermentation

A mathematical model for the batch culture of Clostridium acetobutylicum was formulated using experimental data for anaerobic solvent production. The model summarizes biochemical as well as physiological aspects of growth and metabolite synthesis by the production strain. The key fermentation rates are expressed and evaluated with regard to substrate consumption and butanol end-product inhibitory effects. Parametric sensitivity analysis of the batch process model was carried out, indicating the importance of the key process parameters.     

Analysis of Chinese hamster ovary cell metabolism through a combined computational and experimental approach

Optimization of cell culture processes can benefit from the systematic analysis of experimental data and their organization in mathematical models, which can be used to decipher the effect of individual process variables on multiple outputs of interest. Towards this goal, a kinetic model of cytosolic glucose metabolism coupled with a population-level model of Chinese hamster ovary cells was used to analyse metabolic behavior under batch and fed-batch cell culture conditions. The model was parameterized using experimental data for cell growth dynamics, extracellular and intracellular metabolite profiles. The results highlight significant differences between the two culture conditions in terms of metabolic efficiency and motivate the exploration of lactate as a secondary carbon source. Finally, the application of global sensitivity analysis to the model parameters highlights the need for additional experimental information on cell cycle distribution to complement metabolomic analyses with a view to parameterize kinetic models.     

Modeling and observer design for recombinant Escherichia coli strain

A mathematical model for recombinant bacteria which includes foreign protein production is developed. The experimental system consists of an Escherichia Coli strain and plasmid pIT34 containing genes for bioluminescence and production of a protein, β-galactosidase. This recombinant strain is constructed to facilitate on-line estimation and control in a complex bioprocess. Several batch experiments are designed and performed to validate the developed model. The design of a model structure, the identification of the model parameters and the estimation problem are three parts of a joint design problem. A nonlinear observer is designed and an experimental evaluation is performed on a batch fermentation process to estimate the substrate consumption.     

Mathematical modeling of wastewater decolorization in a trickle-bed bioreactor

This work focuses on mathematical modeling of removal of organic dyes from textile industry waste waters by a white-rot fungus Irpex lacteus in a trickle-bed bioreactor. We developed a mathematical model of biomass and decolorization process dynamics. The model comprises mass balances of glucose and the dye in a fungal biofilm and a liquid film. The biofilm is modeled using a spatially two-dimensional domain. The liquid film is considered as homogeneous in the direction normal to the biofilm surface. The biomass growth, decay and the erosion of the biofilm are taken into account. Using experimental data, we identified values of key model parameters: the dye degradation rate constant, biofilm corrugation factor and liquid velocity. Considering the dye degradation rate constant 1×10?? kg m?3 s?1, we found optimal values of the corrugation factor 0.853 and 0.59 and values of the liquid velocity 5.23×10?3?m?s?1 and 6.2×10?3?m?s?1 at initial dye concentrations 0.09433 kg m?3 and 0.05284 kg m?3, respectively. A good agreement between the simulated and experimental data using estimated values of the model parameters was achieved. The model can be used to simulate the performance of laboratory scale trickle-bed bioreactor operated in a batch regime or to estimate values of principal parameters of the bioreactor system.     

Unstructured models for growth and lactic acid production during two-stage continuous cultures of Lactobacillus helveticus

During lactic acid fermentation, seed culture is usually carried out without pH control, while culture is carried out at pH controlled at the optimal value to overcome inhibitory effects. The Luedeking–Piret expression was therefore previously modified by introducing additional terms involving the undissociated form of the lactic acid, the main inhibitory species, in case of batch cultures without pH control or involving the residual lactose concentration to account for the carbon substrate limitation, responsible for cessation of production during batch cultures of Lactobacillus helveticus at controlled pH. Both expressions were also merged to deduce a generalized model. Both models, as well as the Luedeking–Piret model, were developed to describe continuous two-stage culture of L. helveticus. By considering the parameter values obtained from the fitting of batch culture data, both modified Luedeking–Piret models showed interesting predictive potential. Indeed, some rather reliable predictive calculated values were recorded in both stages; the residual standard deviations were 0.5 and less than 8.8 for the biomass and the product concentrations at steady-state in the culture stage (second stage). The optimization of the parameters for growth- and non-growth-associated parameters improved the fitting in the culture stage, leading to residual standard deviations below 2.6 for lactic acid concentrations at steady-state.     

Maximizing production of Penicillium cyclopium partial acylglycerol lipase

Penicillium cyclopium partial acylglycerol lipase production was maximized in shaken batch culture. The effect of inoculum size and substrate concentration on the lipase activity released in the culture medium was visualized using a surface response methodology based on a Doehlert experimental design. The main advantage of this approach is the low number of experiments required to construct a predictive model of the experimental domain. Substrate percentage (corn steep, w/v) ranged from 0.1% to 1.9% and inoculum from 100 spores/ml to 3,200 spores/ml. We determined that an optimal set of experimental conditions for high lipase production was 1.0% substrate and 3,200 spores/ml, with initial pH 5.0, temperature 25 degrees C and shaking speed 120 rpm. Between the conditions giving the minimum and the maximum lipase production, we observed a three-fold increase in both the predicted and the measured values.     

A simple structured mathematical model for biopolymer (PHB) production

Economic production technology for a biodegradable polymer (poly-beta-hydroxybutyrate, PHB) is urgently required to replace conventional polymers, which have an inherent disadvantage of staying in the environment forever. Various approaches have been applied for improving the productivity and reducing the production cost, which are considered to be the two major problems associated with industrial production of PHB. One of the engineering approaches to improve PHB productivity could be to design and implement model-based fed-batch cultivations to provide desirable nutrient availability. In the present study, growth and intracellular biopolymer storage kinetics of Ralstonia eutropha was studied in a batch cultivation process. It featured 19.7 g/L biomass and 10.89 g/L PHB with a productivity of 0.18 g/L.h. The effect of carbon, nitrogen, and phosphate limitations and inhibitions on growth was studied in detail. A structured model featuring typical growth limitations and/or possible inhibitions was then proposed. The value of the model parameters was found by minimizing the difference between experimental value and model simulation at all data points and for all process variables. The optimal batch model parameter values obtained above were used to solve the differential equations numerically. The simulated data obtained in this way was then compared with the experimental data to establish the validity of the batch model. The proposed model was then compared with literature reported mathematical models to reconfirm its accuracy. Statistical validity of the developed model and historical models to describe the observed experimental kinetics was then investigated to reinforce the accuracy of the developed simple model.     

双碳源单细胞蛋白间歇培养及流加培养的动力学模型

应用非结构的逻辑增殖模型研究了两种酵母的单碳源和双碳源单细胞蛋白间歇培养的动力学,用改进的逻辑增殖模型研究了双碳源流加培养过程的动力学,从实验数据拟合了动力学模型参数,模型计算值与实验数据吻合良好。     

Spreadsheet Method for Evaluation of Biochemical Reaction Rate Coefficients and Their Uncertainties by Weighted Nonlinear Least-Squares Analysis of the Integrated Monod Equation

A convenient method for evaluation of biochemical reaction rate coefficients and their uncertainties is described. The motivation for developing this method was the complexity of existing statistical methods for analysis of biochemical rate equations, as well as the shortcomings of linear approaches, such as Lineweaver-Burk plots. The nonlinear least-squares method provides accurate estimates of the rate coefficients and their uncertainties from experimental data. Linearized methods that involve inversion of data are unreliable since several important assumptions of linear regression are violated. Furthermore, when linearized methods are used, there is no basis for calculation of the uncertainties in the rate coefficients. Uncertainty estimates are crucial to studies involving comparisons of rates for different organisms or environmental conditions. The spreadsheet method uses weighted least-squares analysis to determine the best-fit values of the rate coefficients for the integrated Monod equation. Although the integrated Monod equation is an implicit expression of substrate concentration, weighted least-squares analysis can be employed to calculate approximate differences in substrate concentration between model predictions and data. An iterative search routine in a spreadsheet program is utilized to search for the best-fit values of the coefficients by minimizing the sum of squared weighted errors. The uncertainties in the best-fit values of the rate coefficients are calculated by an approximate method that can also be implemented in a spreadsheet. The uncertainty method can be used to calculate single-parameter (coefficient) confidence intervals, degrees of correlation between parameters, and joint confidence regions for two or more parameters. Example sets of calculations are presented for acetate utilization by a methanogenic mixed culture and trichloroethylene cometabolism by a methane-oxidizing mixed culture. An additional advantage of application of this method to the integrated Monod equation compared with application of linearized methods is the economy of obtaining rate coefficients from a single batch experiment or a few batch experiments rather than having to obtain large numbers of initial rate measurements. However, when initial rate measurements are used, this method can still be used with greater reliability than linearized approaches.