Unstructured Kinetic Model Research Articles

Physiological modelling of the response of Kocuria rosea exposed to changing water activity

Physiological effects of NaCl concentration (equivalent water activities, aw, 1 to 0.87) were investigated with the moderately halophilic and piezotolerant bacterium, Kocuria rosea (formerly Micrococcus roseus), grown in bacteriological peptone/yeast extract broth. This bacterium, which was isolated from open shallow seawater, can grow in 150 g NaCl l−1 (optimum NaCl concentration: 30 g l−1, aw=0.984) and under 207 MPa of hydrostatic pressure. The effects of water activity on μm can be quantitatively predicted, to a high level of accuracy by application of the Aiba/Edwards, and the Levenspiel-type unstructured inhibition-type kinetic models.

Modeling and advanced control of recombinant Zymomonas mobilis fed-batch fermentation.

This work presents the development of an unstructured kinetic model incorporating the differing degrees of product, substrate, and pH inhibition on the kinetic rates of ethanol fermentation by recombinant Zymomonas mobilis CP4:pZB5 for growth on two substrates. Product inhibition was observed to start affecting the specific growth rate at an ethanol concentration of 20 g/L and the specific productivity at about 35-40 g/L. Specific growth rate was also shown to be more sensitive to inhibition by lowered pH as well. A model for the inhibition of two competing substrates' cellular uptake via membrane transport is proposed. Inhibition functions and model parameters were determined by fitting experimental data to the model. The model was utilized in a nonlinear model predictive control (NMPC) algorithm to control the product concentration during fed-batch fermentation to offset the inhibitory effects of product inhibition. Using the optimal feeding policy determined online, the volumetric productivity of ethanol was improved 16.6% relative to the equivalent batch operation when the final ethanol concentration was reached.

NONLINEAR MPC FOR RECOMBINANT ZYMOMONAS MOBILIS FED-BATCH ETHANOL FERMENTATION

This work presents the development of an unstructured kinetic model incorporating the differing degrees of product inhibition on the kinetic rates of recombinant Zymomonas mobilis fermentation. A mechanism for the inhibition of two competing substrates cellular uptake via membrane transport is proposed. The model was utilized in a nonlinear model predictive control (NMPC) algorithm to control product concentration during fed-batch fermentation. Using optimal feeding policy determined online by the NMPC controller, the volumetric productivity of ethanol was improved by 16.6% relative to the equivalent batch operation when the same final ethanol concentration was reached.

Periodic behaviour of a class of unstructured kinetic models for continuous bioreactors

AbstractThe periodic behaviour of a large dass of unstructured kinetic models for continuous bioreactors is analyzed using elementary concepts of singularity theory and continuation techniques. The class consists of models for which the utilization rate of the limiting substrate is linearly related to the rates of cell growth and product formation. The model kinetics are allowed, on the other hand, to depend on substrate, biomass and product. The stability analysis allows the derivation of general analytical conditions for the occurrence of periodic behaviour in these models. It is shown that for a number of important cases, the occurrence of oscillatory behaviour is conditioned mainly by the kinetics of product formation. The singularity theory also allows the construction of a useful picture in the multidimensional parameter space delineating the different behaviour these models can predict including bistability and stable oscillatory behaviour.

Determination of the maximum specific uptake capacities for glucose and oxygen in glucose-limited fed-batch cultivations of Escherichia coli.

A simple pulse-based method for the determination of the maximum uptake capacities for glucose and oxygen in glucose limited cultivations of E. coli is presented. The method does not depend on the time-consuming analysis of glucose or acetate, and therefore can be used to control the feed rate in glucose limited cultivations, such as fed-batch processes. The application of this method in fed-batch processes of E. coli showed that the uptake capacity for neither glucose nor oxygen is a constant parameter, as often is assumed in fed-batch models. The glucose uptake capacity decreased significantly when the specific growth rate decreased below 0.15 h(-1) and fell to about 0.6 mmol g(-1) h(-1) (mmol per g cell dry weight and hour) at the end of fed-batch fermentations, where specific growth rate was approximately 0.02 h(-1). The oxygen uptake capacity started to decrease somewhat earlier when specific growth rate declined below 0.25 h(-1) and was 5 mmol g(-1) h(-1) at the end of the fermentations. The behavior of both uptake systems is integrated in a dynamic model which allows a better fitting of experimental values for glucose in fed-batch processes in comparison to generally used unstructured kinetic models.

Solving Dual Optimization Problems in Identification and Performance of Fed-Batch Bioreactors

In this paper some aspects of the duality found within the following two tightly interconnected problems are discussed: (i) (model based) process performance optimization, and (ii) information content optimization for model identification. In the two case studies presented, the volumetric substrate feed rate into a fedbatch bioreactor in which one biomass grows on one limiting substrate is the control input to be optimized. Unstructured kinetic models in which the specific growth rate is a function of the substrate concentration only are considered. In case study #1 the optimization of a cost criterion combining both a performance cost and a parameter identification cost is discussed. Case study #2 is entirely devoted to information content optimization. A novel combined input design criterion for parameter estimation is constructed. For specific values of the weighting factor, it reduces to the modified E-criterion, the E-criterion, or the D-criterion.

Studies on fermentation with recombinant yeast cells: plasmid stability and kinetics of biomass and protein production

Plasmid stability of the recombinant Saccharomyces cerevisiae YPB-G strain harbouring a YEp plasmid with α-amylase and glucoamylase genes as a fusion has been investigated in shake flasks and in a bioreactor using various compositions of media containing glucose or starch as the main carbon source. The medium composition affected both the growth characteristics and the stability of the plasmid. Superior plasmid stability was obtained in yeast minimal medium and in complex medium with glucose. Plasmid stability was substantially increased at high growth rates. Additional data were collected in the same system to investigate the kinetic characteristics of biomass and protein production, and unstructured kinetic models were used to interpret the results. At high initial glucose concentrations, where the biomass and protein production rates were similar, the kinetic models displayed good fits associated with high degrees of correlation.

Production of an Alcoholic Beverage by Fermentation of Whey Permeate withKluyveromyces fragilisI: Primary Metabolism

Whey permeate from the ultrafiltration processing of cheese manufacturing was used for alcoholic fermentation with Kluyveromyces fragilis, the objective being the production of an alcoholic beverage of low alcoholic grade. The effect of temperature, initial pH, agitation and initial biomass on yeast growth and ethanol production were assayed in batch cultures. In addition, continuous culture behaviour was studied due to interest in a continuous industrial process for a new product. An unstructured kinetic model (a Riccati kinetic equation) is proposed; batch data being employed to obtain the kinetic parameters. This model fits the continuous culture results well except for ethanol production, where calculated values were lower than experimental data. When the fermentation temperature was changed from 18 to 37°C, a maximum of YP/S close to 30°C was observed, which gives an efficiency in the conversion of lactose to ethanol of 88%. The initial pH of the whey did not affect yeast growth significantly. Experiments carried out at different initial biomass concentrations showed that an initial dry weight close to 0.5 g/litre was sufficient to carry out the fermentation. An increase in ethanol concentrations was found at higher rates of agitation. In continuous culture, a maximum productivity for biomass and ethanol was attained at a dilution rate of 0.11 h−1. Higher efficiencies (96%) were achieved in continuous culture rather than in batch cultivation mode.

A kinetic model for lutein production by the green microalga Chlorella protothecoides in heterotrophic culture

Production of lutein by the green microalga Chlorella protothecoides grown heterotrophically in a fermentor using glucose as the carbon source and urea as the nitrogen source was investigated. An unstructured kinetic model was proposed to describe the microalgal culture system including cell growth, lutein formation, as well as glucose and nitrogen consumption. The inhibition potentials of biomass, product and substrates on growth and lutein formation were examined and incorporated into the kinetic model. Values of the kinetic model parameters were estimated. The resulting model predictions were in good agreement with the experimental results. The model can be helpful in scale-up, optimization and control of the C. protothecoides culture process, and can also be used as a guideline for similar microalgal cultivation systems.

An unstructured kinetic model of macromolecular metabolism in batch and fed-batch cultures of hybridoma cells producing monoclonal antibody

Growth profiles of the batch and fed-batch culture of hybridoma cells producing monoclonal antibody were simulated using an unstructured model. The model describes the production of cellular macromolecules and monoclonal antibody, the metabolism of glucose and glutamine with the production of lactate and ammonia, and the profiles of cell growth in batch and fed-batch culture. Equations describing the cells arrested in G1 phase [T.I. Linardos, N. Kalogerakis, L.A. Behie, Biotechnol. Bioeng. 40 (1992) 359–368; E. Suzuki, D.F. Ollis, Biotechnol. Bioeng. 34 (1989) 1398–1402] were included in this model to describe the increase of the specific antibody productivity in the near-zero specific growth rate, which was observed in the recent experiments in fed-batch cultures of this study and the semi-continuous culture of hybridoma cells [S. Reuveny, D. Velez, L. Miller, J.D. Macmillan, J. Immnol. Methods 86 (1986) 61–69]. This model predicted the increase of specific antibody production rate and the decline of the specific production rate of cellular macromolecules such as DNA, RNA, protein, and polysaccharide in the late exponential and decline phase of batch culture and at lower specific growth rates in the fed-batch culture.

Unstructured kinetic model for sophorolipid production by Candida bombicola

A kinetic model for sophorolipid production by Candida bombicola is proposed. The unstructured nonsegregated kinetic model takes into account three responses: biomass, sugar, and sophorolipid. In the kinetic model, the nitrogen—from yeast extract—is assumed to be the limiting nutrient of the yeast growth, the sugar—glucose—is assumed to be used in both growth and sophorolipid production, and oil is supposed to be spent in product formation and maintenance of biomass is attributed to glycerol eased by the catabolism of the oil. The parameters of the kinetic model are calculated by fitting model to experimental data. These data have been obtained in experiments in which a batch stirred and an aerated tank bioreactor have been used. Fitting has been carried out according to a nonlinear regression algorithm, coupled with a Runge–Kutta method for the interpretation of integral data (evolution of system composition with time). The proposed kinetic model is able to explain both our experimental data and data given by other authors in previous works in literature in which nutrient and product concentrations evolution are given.

Kinetic models for astaxanthin production by high cell density mixotrophic culture of the microalga Haematococcus pluvialis.

High cell density cultivation of Haematococcus pluvialis for astaxanthin production was carried out in batch and fed-batch modes in 3.7-L bioreactors with stepwise increased light intensity control mode. A high cell density of 2.65 g x L(-1) (batch culture) or 2.74 g x L(-1) (fed-batch culture) was obtained, and total astaxanthin production in the fed-batch culture (64.36 mg x L(-1)) was about 20.5% higher than in the batch culture (53.43 mg x L(-1)). An unstructured kinetic model to describe the microalga culture system including cell growth, astaxanthin formation, as well as sodium acetate consumption was proposed. Good agreement was found between the model predictions and experimental data. The models demonstrated that the optimal light intensity for mixotrophic growth of H. pluvialis in batch or fed-batch cultures in a 3.7-L bioreactor was 90-360 micromol x m(-2) x s(-1), and that the stepwise increased light intensity mode could be replaced by a constant light intensity mode.

FEED RATE OPTIMIZATION FOR FED-BATCH BIOREACTORS: FROM OPTIMAL PROCESS PERFORMANCE TO OPTIMAL PARAMETER ESTIMATION

In this paper the optimization of a cost criterion combining both a performance cost and a parameter identification cost is discussed for the growth of biomass on one limiting substrate in a fed-batch bioreactor. Both monotonic and non-monotonic unstructured kinetic models in which the specific growth rate is a function of the substrate concentration only are considered. The parametric optimization of the feed rate profile in the fed-batch bioreactor with respect to a novel combined cost function yields a continuous transformation of the optimal performance feed rate profile towards the optimal identification profile as more weight is assigned to the identification purpose. As such we provide support for the conjecture that a feed rate strategy which is optimal in the sense of process performance, is an excellent starting point for feed rate optimization with respect to estimation of those parameters with large influence upon process performance.

Influence of the nitrogen source on the production and rheological properties of scleroglucan produced by Sclerotium rolfsii ATCC 201126

Scleroglucan production by Sclerotium rolfsii ATCC 201126 has been studied using nitrate or ammonium as nitrogen sources at several concentrations. In all the experiments carried out, both growth and production were modelled by an unstructured kinetic model using logistic and Luedeking–Piret equations for describing growth and production, respectively. The kinetic parameters for growth (μ and YXN) and for production (α and β) were obtained by fitting the data to the model using the single-response non-linear regression technique by means of the algorithm of Marquardt coupled to a fourth-order Runge–Kutta algorithm. Biomass and scleroglucan production were higher when nitrate was the nitrogen source. Rheological properties of scleroglucan produced using nitrate as nitrogen source were studied and rheological parameters calculated, revealing similarity between this biopolymer and commercial scleroglucan.

Kinetic models for phycocyanin production by high cell density mixotrophic culture of the microalga Spirulina platensis

Phycocyanin production by high cell density cultivation of Spirulina platensis in batch and fed-batch modes in 3.7-L bioreactors with a programmed stepwise increase in light intensity program was investigated. The results showed that the cell density in fed-batch culture (10.2 g L−1) was 4.29-fold that in batch culture (2.38 g L−1), and the total phycocyanin production in the fed-batch culture (0.795 g L−1) was 3.05-fold that in the batch culture (0.261 g L−1). An unstructured kinetic model to describe the microalga culture system including cell growth, phycocyanin formation, as well as glucose consumption was proposed. The data fitted the models well (r2 > 0.99). Furthermore, based on the kinetic models, the potential effects of light limitation and photoinhibition on cell growth and phycocyanin formation can be examined in depth. The models demonstrated that the optimal light intensity for mixotrophic growth of Spirulina platensis in batch or fed-batch cultures using a 3.7-L bioreactor was 80160 μE m−2 s−1, and the stepwise increase in light intensity can be replaced by a constant light intensity mode.

Xanthan gum production: An unstructured kinetic model

Xanthan production was studied in a stirred-tank fementor and modeled using unstructured kinetic models. First, the influences of the operational conditions have been studied. Temperature (between 22 and 34°C), aeration (changing stirrer speed between 150 and 1,000 rpm, maintained at constant or varied through fermentation time), and the pH control (with two alkalis) were analyzed. Then, unstructured kinetic models proposed in the literature for this system were reviewed and applied. These models have been checked to describe the experimental results, calculating the parameters by nonlinear regression. The results show that these models do not take into account all the necessary nutrients, which are carbon source, nitrogen source, and dissolved oxygen. Afterward, an unstructured kinetic model describing biomass, carbon source, nitrogen source, and dissolved oxygen evolutions was proposed and applied. Parameters estimation were carried out by means of both differential and integral methods. Parameters values were finally obtained applying an integral method using non-linear regression techniques. The model proposed in this work is composed of five differential equations with production rates of the five components taken into account: biomass, carbon, and nitrogen sources, xanthan, and dissolved oxygen, capable of fitting all the three experiments considered, at different temperatures and controlling and not controlling pH.

Effect of some physico‐chemical treatments on the kinetics of autolysed‐yeast extract production from whey

AbstractIn this work, the effects of salt and mechanical cell breaking on the overall activity of the endogenous enzymes of Kluyveromyces fragilis grown on whey‐based media were studied at the optimal values of temperature (54°C) and initial concentration of yeast and whey protein (100 g dm−3) previously selected. An unstructured kinetic model of first order was found to be capable of simulating quite satisfactorily the time course of residual suspended solids (Y) in the slurry, as well as Kjeldahl (KP) and Lowry (LP) protein and total carbohydrates (G) accumulation in the clear extract. The autolysis kinetic rate constant (ka), and yield factors for Kjeldahl and Lowry protein and reducing sugars on total solids hydrolysed were found to be insensitive to the salt level and preliminary mechanical disruption of cells. Nevertheless, maximum production of yeast‐whey protein extracts was achieved when the endogenous enzymes of ground cells are induced by 5% w/v salt addition. Except for their respective salt contents, both autolysates exhibited no apparent difference in chemical composition.

A kinetic model for the fungal pellet lifecycle

AbstractMany industrially significant microbial products are produced during secondary metabolism by fungal pellets. Most models of mycelial pellet growth, however, consider only the primary growth phase. During secondary metabolism, the whiterot fungus Phanerochaete chrysosporium produces extra‐cellular lignin peroxidases and manganese‐dependent peroxidases which have been implicated in the degradation of lignin and various xenobiotics. This unstructured kinetic model for mycelial pellet cultures of P. chrysosporium describes the culture dry weight, respiration, glucose consumption, nutrient nitrogen uptake, pellet size and oxygen effectiveness factor during the lag, primary growth, secondary metabolic, and death phases. During secondary metabolism, the intraparticle diffusion of oxygen limits metabolism. Parameters for respiration during secondary metabolism are validated using three separate measurements: 1. by measuring oxygen concentration profiles in mycelial pellets using oxygen microelectrodes; 2. by measuring the depletion of oxygen from the culture fluid using a respirometer; and 3. by measuring the daily evolution of carbon dioxide. The physiological state of the mycelial pellets is predicted for various culture conditions and is related to the production of LIP and MNP during secondary metabolism.

Chemostat cultures of yeasts, continuous culture fundamentals and simple unstructured mathematical models

Fundamental aspects of chemostat cultures are reviewed. Using yeast cultures as examples, it is shown that steady states in chemostats may be predicted quantitatively by combining the correct number of unstructured kinetic models with expressions for existing stoichiometric constraints. The necessary number of such kinetic models corresponds to the number of limiting substrates and increases with the number of different metabolic pathways available to the strain. This is demonstrated by an experimental comparison of yeast growth limited by glucose alone for which metabolism is oxidative, and growth doubly limited by both glucose and oxygen, which occurs according to an oxido-reductive metabolism. The steady state data for such experiments can in principle be predicted based on a minimal amount of information by a simple stoichiometric model. It represents the overall stoichiometry of growth by a superposition of a fully oxidative and a fully reductive growth reaction and uses the concept of “aerobicity” to characterize the relative importance of the two reactions.

Characterization of an Immobilized Biocatalyst System for Production of Thermostable Amylase

AbstractAn immobilized biocatalyst system for enzyme production using a thermophilic organism is described. Bacillus stearothermophilus (ATCC 29609) immobilized on Rohm and Haas IRA–938 ion exchange resin was utilized for the production of a highly thermostable α‐amylase in a bench scale airlift fermentor. The equilibrium between suspended bacterial cells and the resin fit a Langmuir‐type sorption isotherm. Cell and α‐amylase productivity data for free cell and immobilized cell continuous culture were compared as functions of the dilution rate. Cell growth rates for free and immobilized cells were consistent with the Monod kinetic model, α‐Amylase production for free cells was described by an unstructured model associated with cell growth. The immobilized cell systems gave higher α‐amylase productivity than the free cell system but did not achieve the productivities predicted by the unstructured kinetic model.