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.     

Unstructured model for free and immobilized cell culture without pH control of Bifidobacterium animalis subsp. lactis Bb 12—Inhibitory effect of the undissociated organic acids

A model was developed to describe growth and organic acids production of Bifidobacterium animalis growing without pH control in free and immobilized cell culture. The Verlhust model was considered for growth, and to account for the inhibition observed at acidic pH, the Luedeking–Piret production model was modified by introducing an additional term involving the undissociated form of the organic acids, acetic and lactic acids, the main inhibitory species. To describe the relationship between pH and both the dissociated and the undissociated forms of organic acids, the Henderson–Hasselbach equation was considered. The model was found to satisfactory describe experimental growth and production data recorded during free and immobilized cell cultures. The part of each acid produced can be deduced from the calculated production data, since a constant lactic to acetic acid mass ratio was found, 1.29 and 1.66 during free and immobilized cell cultures. Owing to the acidic pH values recorded, 4.43 at lowest, higher amounts of undissociated acetic acid were produced, leading to a higher inhibitory effect of this acid if compared to lactic acid.     

A segregated model for heterologous amylase production by Bacillus subtilis

A segregated model was proposed to investigate the inherent relationships between growth, substrate consumption, cell differentiation and product formation in a Bacillus subtilis fermentation producing heterologous amylase in a 22-l bioreactor. The segregated model includes three distinguishable cell states and the transition from vegetative phase to sporangium and finally to mature spore. An age-based population balance model was applied to describe the maturity of sporangium toward the formation of spores. Parameters in the model were determined by fitting the model with experimental data. The model was able to predict the transient behavior of B. subtilis in both batch and fed-batch cultures.     

Modelling and simulation of cell growth dynamics, substrate consumption, and lactic acid production kinetics of Lactococcus lactis

Lactococcus lactis species have been and still are extensively investigated due to their significant commercial importance. Current scientific research focuses on strains utilized in food industry, due to their multiple uses in food and beverages fabrication. Biomass of Lactococcus lactis is of great interest as well as the end products of its metabolism such as lactic acid and nisin. However their production is constantly challenged due to end product inhibition occurring during intensive propagation of the coccus in reactor systems. To successfully predict the behavior of the culture, the approach of combining mathematics with biology, ergo the development of an unstructured mathematical model, was taken. Although Luedeking and Piret is the model that has been extensively used to demonstrate growth in end-product inhibition cultures, its applicability is limited due to its dependance on the specific growth and product coefficients, particularly related to the culturing conditions used. To overcome these hurdles, a combination of the non competitive single product end inhibition Taylor and Hinselwood models was used, with the significance of this model laying in the fact that it offers a feasible alternative to the commonly used model of Luedeking and Piret for describing fermentation kinetics governed by end-product inhibitions. The fitting with the experimental values, in batch mode, was tested in terms of the coefficient of determination (R²), having values 0.97 ～ 0.99 and suggesting a very good fitting with the experimental data. The model was further developed to achieve theoretical predictions of volumetric cell productivity in continuous and fed-batch mode of substrate feed in different culturring systems.     

Modeling the specific growth rate of Lactobacillus plantarum in cucumber extract

Extensive empirical research has been published on the fermentation of vegetables, but little predictive modeling of the process is available. The objectives of this study were to assess the effects of key variables involved in cucumber fermentation and to develop models for predicting the growth of Lactobacillus plantarum in pure and mixed culture fermentations. The growth medium for the studies was cucumber juice. The effects of various concentrations of lactic, acetic, and hydochloric acids and sodium chloride on growth at 30° C were determined in batch culture. Limiting conditions for growth were pH 3.37 (lower limit), 69 mm undissociated lactic acid, 150 mm undissociated acetic acid, or 11.8% NaCl. Acetic acid was stimulatory to growth at low concentrations (up to 40 mm) but inhibitory at higher concentrations. Lactic acid was more inhibitory than acetic acid, whether total or undissociated concentrations were used as the basis of comparison. A predictive equation for specific growth rate was developed, tested, and shown to predict growth of L. plantarum in batch processes reasonably well.Mention of a trademark or proprietary product does not constitute a guarantee or warranty of the product by the U. S. Department of Agriculture or North Carolina Agricultural Research Service, nor does it imply approval to the exclusion of other products that may be suitable Correspondence to: H. P. Fleming     

Uncoupling by Acetic Acid Limits Growth of and Acetogenesis by Clostridium thermoaceticum

When cells of the anaerobic thermophile Clostridium thermoaceticum grow in batch culture and homoferment glucose to acetic acid, the pH of the medium decreases until growth and then acid production cease, at about pH 5. We postulated that the end product of fermentation limits growth by acting as an uncoupling agent. Thus, when the pH of the medium is low, the cytoplasm of the cells becomes acidified below a tolerable pH. We have therefore measured the internal pH of growing cells and compared these values with those of nongrowing cells incubated in the absence of acetic acid. Growing cells maintained an interior about 0.6 pH units more alkaline than the exterior throughout most of batch growth (i.e., ΔpH = 0.6). We also measured the transmembrane electrical potential (ΔΨ), which decreased from 140 mV at pH 7 at the beginning of growth to 80 mV when the medium had reached pH 5. The proton motive force, therefore, was 155 mV at pH 7, decreasing to 120 mV at pH 5. When further fermentation acidified the medium below pH 5, both the ΔpH and the ΔΨ collapsed, indicating that these cells require an internal pH of at least 5.5 to 5.7. Cells harvested from stationary phase and suspended in citrate-phosphate buffer maintained a ΔpH of 1.5 at external pH 5.0. This ΔpH was dissipated by acetic acid (at the concentrations found in the growth medium) and other weak organic acids, as well as by ionophores and inhibitors of glycolysis and of the H⁺-ATPase. Nongrowing cells had a ΔΨ which ranged from about 116 mV at external pH 7 to about 55 mV at external pH 5 and which also was sensitive to ionophores. Since acetic acid, in its un-ionized form, diffuses passively across the cytoplasmic membrane, it effectively renders the membrane permeable to protons. It therefore seems unlikely that mutations at one or a few loci would result in C. thermoaceticum cells significantly more acetic acid tolerant than their parental type.     

Modelling and validation of Lactobacillus plantarum fermentations in cereal-based media with different sugar concentrations and buffering capacities

An unstructured mathematical model is proposed to describe the fermentation kinetics of growth, lactic acid production, pH and sugar consumption by Lactobacillus plantarum as a function of the buffering capacity and initial glucose concentration of the culture media. Initially the experimental data of L. plantarum fermentations in synthetic media with different buffering capacity and glucose were fitted to a set of primary models. Later the parameters obtained from these models were used to establish mathematical relationships with the independent variables tested. The models were validated with 6 fermentations of L. plantarum in different cereal-based media. In most cases the proposed models adequately describe the biochemical changes taking place during fermentation and are a promising approach for the formulation of cereal-based probiotic foods.     

Modeling of an integrated fermentation/membrane extraction process for the production of 2-phenylethanol and 2-phenylethylacetate

An unstructured model for an integrated fermentation/membrane extraction process for the production of the aroma compounds 2-phenylethanol and 2-phenylethylacetate by Kluyveromyces marxianus CBS 600 was developed. The extent to which this model, based only on data from the conventional fermentation and separation processes, provided an estimation of the integrated process was evaluated. The effect of product inhibition on specific growth rate and on biomass yield by both aroma compounds was approximated by multivariate regression. Simulations of the respective submodels for fermentation and the separation process matched well with experimental results. With respect to the in situ product removal (ISPR) process, the effect of reduced product inhibition due to product removal on specific growth rate and biomass yield was predicted adequately by the model simulations. Overall product yields were increased considerably in this process (4.0 g/L 2-PE+2-PEA vs. 1.4 g/L in conventional fermentation) and were even higher than predicted by the model. To describe the effect of product concentration on product formation itself, the model was extended using results from the conventional and the ISPR process, thus agreement between model and experimental data improved notably. Therefore, this model can be a useful tool for the development and optimization of an efficient integrated bioprocess.     

Kinetics of substrate consumption and product formation in closed acetic fermentation systems

This paper proposes a kinetic model for substrate consumption and product formation, in low alcohol media, of Acetobacter aceti in submerged culture. The model considers ethanol consumption for growth of biomass and formation of secondary products by a chemical route. Experimental data were obtained in the laboratory using a variety of discontinuous fermentation apparatus with automatic control, and either open or closed gas recirculation systems. Operating conditions applied were those typical of acetic fermentation process in the food industry. The fit of equations to the experimental data gives high theoretical-experimental determination coefficients.     

Acetic Acid Production by an Electrodialysis Fermentation Method with a Computerized Control System

In acetic acid fermentation by Acetobacter aceti, the acetic acid produced inhibits the production of acetic acid by this microorganism. To alleviate this inhibitory effect, we developed an electrodialysis fermentation method such that acetic acid is continuously removed from the broth. The fermentation unit has a computerized system for the control of the pH and the concentration of ethanol in the fermentation broth. The electrodialysis fermentation system resulted in improved cell growth and higher productivity over an extended period; the productivity exceeded that from non-pH-controlled fermentation. During electrodialysis fermentation in our system, 97.6 g of acetic acid was produced from 86.0 g of ethanol; the amount of acetic acid was about 2.4 times greater than that produced by non-pH-controlled fermentation (40.1 g of acetic acid produced from 33.8 g of ethanol). Maximum productivity of electrodialysis fermentation in our system was 2.13 g/h, a rate which was 1.35 times higher than that of non-pH-controlled fermentation (1.58 g/h).     

Kinetics and mathematical modeling of homoacetic fermentation of lactate by Clostridium formicoaceticum

Fermentation kinetics of Clostridium formicoaceticum grown on lactate at pH 7.0 and 35 degrees C was studied. Acetate was the only fermentation product and its production was growth associated. The growth of this bacterium was insensitive to the lactate concentrations studied, but was inhibited by acetic acid. A Monod-type expression with product inhibition similar to the noncompetitive inhibition of enzyme kinetics was used to model the batch fermentation. An integrated equation was developed and used to help estimating the kinetic parameters in the model. This mathematical model can be used to simulate the homoacetic fermentation of lactate by C. formicoaceticum at pH 7.0 and 35 degrees C.     

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.     

Energy-Based Dynamic Model for Variable Temperature Batch Fermentation by Lactococcus lactis

We developed a mechanistic mathematical model for predicting the progression of batch fermentation of cucumber juice by Lactococcus lactis under variable environmental conditions. In order to overcome the deficiencies of presently available models, we use a dynamic energy budget approach to model the dependence of growth on present as well as past environmental conditions. When parameter estimates from independent experimental data are used, our model is able to predict the outcomes of three different temperature shift scenarios. Sensitivity analyses elucidate how temperature affects the metabolism and growth of cells through all four stages of fermentation and reveal that there is a qualitative reversal in the factors limiting growth between low and high temperatures. Our model has an applied use as a predictive tool in batch culture growth. It has the added advantage of being able to suggest plausible and testable mechanistic assumptions about the interplay between cellular energetics and the modes of inhibition by temperature and end product accumulation.     

Elucidation of Growth Inhibition and Acetic Acid Production by Clostridium thermoaceticum

The production of acetic acid by Clostridium thermoaceticum was studied by using batch fermentations. In a pH-controlled fermentation with sodium hydroxide (pH 6.9), this organism was able to produce 56 g of acetic acid per liter. On the other hand, when the pH was not controlled and was decreased during fermentation to 5.4, the maximum attainable acetic acid concentration was only 15.3 g/liter. To obtain a better understanding of the end product inhibition, various salts were tested to determine their effect on the growth rate of C. thermoaceticum. An inverse linear relationship between the growth rate and the final cell concentration to the sodium acetate concentration was found. By using different concentrations of externally added sodium salts, the relative growth inhibition caused by the anion was found to be in the order of acetate > chloride > sulfate. Various externally added cations of acetate were also examined with respect to their inhibitory effects on growth. The relative magnitude of inhibition on the growth rate was found to be ammonium > potassium > sodium. The combined results have shown that the undissociated acetic acid was much more inhibitory than the ionized acetate ion. Complete growth inhibition resulted when the undissociated acetic acid concentration was between 0.04 and 0.05 M and when the ionized acetate concentration was 0.8 M. Therefore, at low pH (below 6.0), undissociated acetic acid is responsible for growth inhibition, and at high pH (above 6.0), ionized acetate ion is responsible for growth inhibition.     

Transient growth- and product-formation kinetics of acetic acid bacteria

Rates of growth and product formation under non-stationary conditions were measured in fermentations of industrial acetic acid bacteria. A repeated-batch process, where conditions change rapidly, and a slower shift experiment in CSTR culture were examined. Significant deviations from the steady-state kinetics determined in continuous fermentations were found for cell growth as well as for the formation of acetic acid. Algebraic functions of the inhibiting acid concentration were identified to describe the rates of reaction under stationary conditions. Transient kinetics are modeled by phenomenological differential equations. The data from both the repeated-batch experiments and the CSTR shift is consistently reproduced. Measurements and simulation results are presented in phase diagrams of the reaction rates over the concentration of acetic acid. Due to the dynamic effects, which enhance the transient rates of both growth and product formation, the repeated-batch process is superior to a continuous fermentation in terms of total volumetric productivity and final acid concentration.     

Modeling of ethanol fermentation using Zymomonas mobilis ATCC 10988 grown on the media containing glucose and fructose

A model of ethanol fermentation by Zymomonas mobilis ATCC 10988 on the medium containing glucose and fructose is proposed. This model was developed on the basis of metabolic analysis and many experimental findings. When glucose was used as the substrate, the dependence of the carbon fraction (α) assimilating to biomass on the specific growth rate (μ) could be well correlated to α = 0.25μ + 0.012. This correlation resulted in a novel equation for specific glucose uptake rate, which could describe the Z. mobilis fermentation in both batch and continuous modes. When fructose and glucose were both presented in the liquid medium, the model could predict the uptake of glucose and fructose as well as the formation of biomass, ethanol and sorbitol by Z. mobilis. All parameters used in the model were independently evaluated on the basis of various experimental findings. Good agreement was found between the model predictions and data of Z. mobilis fermentation on media containing both glucose and fructose. The proposed model could also describe the behavior of ethanol fermentation on sucrose medium supplemented with immobilized invertase.     

A model for multiproduct-inhibited growth of Enterobacter aerogenes in 2,3-butanediol fermentation

Summary Ethanol is identified as a strongly inhibitory metabolite in addition to acetic acid and 2,3-butanediol in 2,3-butanediol production by Enterobacter aerogenes. A model is proposed to describe the multiproduct-inhibited growth of E. aerogenes in 2,3-butanediol fermentation. The model is verified with data from anaerobic and microaerobic continuous culture. On the basis of this model the difference in biomass production and product patterns during anaerobic and microaerobic growth of E. aerogenes is discussed. Offprint requests to: W.-D. Deckwer