A structured model of dual-limitation kinetics

A structured model of substrate-utilization kinetics that encompasses dual-limitation conditions, caused by simultaneously low concentrations of the electron donor and the electron acceptor, is developed by incorporating the internal cofactor responses into the kinetic variables. The structured model is based on an assumption that the maximum specific electron-donor-oxidation rate (q(md)) is not a constant, but is linearly controlled by the intracellular chemical potentials, log(NAD/NADH) and log(ATP/ADP . P(i)). Determination of the kinetic parameters for the dual-limitation model, using experimental data from the companion article, verifies that q(md) varies and demonstrates that the NAD/NADH ratio affects q(md) in a positive direction; thus, an increase of the ratio increases the rate of electron-donor utilization. Because the internal NAD/NADH ratio rises with an increase in S(ar) the specific electron-donor-utilization rate is accelerated by high S(a). Since the ratio also increases as the specific electron-donor-utilization rate falls, the specific rate is intrinsically accelerated by the cofactor response when it becomes low due to a depletion of electron donor. Because the cofactor responses upon changes of the external substrate concentrations are systematic, the dual-limitation model can be expressed as a function of only external concentrations of electron donor and electron acceptor, which results in a multiplicative (double-Monod) form. Thus, dual limitation by both substrates reduces the overall reaction rate below the rate expected from single limitation by only one, the most severely limiting, substrate. (c) 1996 John Wiley & Sons, Inc.     

A morphologically structured model for penicillin production.

A morphologically structured model is proposed to describe penicillin production in fed-batch cultivations. The model accounts for the effects of dissolved oxygen on cell growth and penicillin production and variations in volume fractions of abiotic and biotic phases due to biomass formation. Penicillin production is considered to occur in the subapical hyphal cell compartment and to be affected by availability of glucose and oxygen. As it stands, the model provides a wide range of applicability in terms of operating conditions. The model has been tested for various conditions and has given satisfactory results. A series of glucose feeding profiles have been considered to demonstrate the capabilities of the proposed model. It is concluded that the model may be valuable for the interpretation of experimental data collected specifically for metabolic flux analysis during fed-batch cultivation because the elements of measured specific production rates are determined from measurements of the concentrations of the components and their mass balances. The proposed model may be further used for developing control strategies and model order reduction algorithms.     

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.     

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.     

Comparative profiles of fungal alpha amylase production by submerged and surface fermentation

Summary Parameters for the production and recovery of pharmaceutical grade alpha amylase fromAspergillus oryzae SMC strain have been optimized. As compared with a submerged fermentation, a surface fermentation was more economical and allowed a more consistent operation of the process facilities. After storage for 12 months at 4°C, ambient temperature and 37°C, alpha amylase samples retained 100, 61, and 58% of activity respectively.     

A simple structured model for recombinant IDShr protein production in Pichia pastoris

A simple structured model is proposed for the methanol production phase of the iduronate 2-sulphate sulfatase recombinant enzyme (IDShr) in Pichia patoris Mut(+). The model is mainly focused in oxidative stress phenomenon due to methanol consumption and based on extracellular experimental information and the basic knowledge of methanol metabolism in Pichia pastoris yeast (P. pastoris). The model's prediction shows a reasonable accuracy as compared with the experimental data. Likewise, it was proved that this model is able to simulate the production of other recombinant protein in P. pastoris.     

A structured metabolic model for anaerobic and aerobic stoichiometry and kinetics of the biological phosphorus removal process

A structured metabolic model is developed that describes the stoichiometry and kinetics of the biological P removal process. In this approach all relevant metabolic reactions underlying the metabolism, considering also components like adenosine triphosphate (ATP) and nic-otinamide-adenine dinucleotide (NADH(2)) are describedbased on biochemical pathways. As a consequence of the relations between the stoichiometry of the metabolic reactions and the reaction rates of components, the required number of kinetic relations to describe the process is reduced. The model describes the dynamics of the storage compounds which are considered separately from the active biomass. The model was validated in experiments at a constant sludge retention time of 8 days, over the anaerobic and aerobic phases in which the external oncentrations as well as the internal fractions of the relevant components involved in the P-removal process were monitored. These measurements include dissolved acetate, phosphate, and ammonium; oxygen consumption; poly-beta-hydroxybutyrate (PHB); glycogen; and active biomass. The model satisfactorily describes the dynamic behavior of all components during the anaerobicand aerobic phases.(c) 1995 John Wiley & Sons, Inc.     

A structured mechanistic model of the kinetics of enzymatic lysis and disruption of yeast cells

A structured, mechanistic model has been built for the kinetics of yeast cell lysis by microbial cell lytic enzymes, based on an understanding of the two-layer yeast cell wall structure and the properties of yeast-lytic enzyme systems. The model predicts the release of protein, peptides and carbohydrates from four cell structures: the outer and inner wall layers, the cytosol and organelles or proteins present in particles; it also predicts organelle or particle lysis or solubilization and the breakdown of released proteins to peptides. Applications of the model to design and optimization of selective product release are discussed.     

A model for the kinetics of crime

Michaelis-Menten kinetics was applied to processes of victimization. The dependence of the rate of victimization on population density was studied, and it was found that 56% of the variance in this complex social phenomenon may be explained with a one-variable model. The effect of police and the social significance of the rate constants are also discussed.     

A diffusion model for geographically structured populations

Summary A diffusion model is derived for the evolution of a diploid monoecious population under the influence of migration, mutation, selection, and random genetic drift. The population occupies an unbounded linear habitat; migration is independent of genotype, symmetric, and homogeneous. The treatment is restricted to a single diallelic locus without dominance. With the customary diffusion hypotheses for migration and the assumption that the mutation rates, selection coefficient, variance of the migrational displacement, and reciprocal of the population density are all small and of the same order of magnitude, a boundary value problem is deduced for the mean gene frequency and the covariance between the gene frequencies at any two points in the habitat. Supported by the National Science Foundation (Grant No. DEB77-21494).     

A simple structured model for biomass and extracellular enzyme production with recombinant Saccharomyces cerevisiae YPB-G

A simple structured model is proposed for simulating batch cultivation data on growth, substrate utilization, and heterologous enzyme production of recombinant Saccharomyces cerevisiae YPB-G. The enzyme is a fusion protein displaying α-amylase and glucoamylase activities. Cell growth is modulated mainly by intracellular substrate and ethanol concentrations. Intracellular substrate concentration is evaluated by means of the extracellular substrate and biomass concentrations. Extracellular α-amylase and glucoamylase activities are taken to depend on biomass concentration. The nine parameters of the proposed model are determined using nonlinear estimation techniques, and the model is validated against experiments not used in parameter determination. The model developed simulates glucose consumption, cell mass, α-amylase and glucoamylase production in a batch system. Simulation and experimental results are found to be in good agreement. Journal of Industrial Microbiology & Biotechnology (2002) 29, 111–116 doi:10.1038/sj.jim.7000281 Received 07 January 2002/ Accepted in revised form 22 May 2002     

A biochemically structured model for Saccharomyces cerevisiae.

A biochemically structured model for the aerobic growth of Saccharomyces cerevisiae on glucose and ethanol is presented. The model focuses on the pyruvate and acetaldehyde branch points where overflow metabolism occurs when the growth changes from oxidative to oxido-reductive. The model is designed to describe the onset of aerobic alcoholic fermentation during steady-state as well as under dynamical conditions, by triggering an increase in the glycolytic flux using a key signalling component which is assumed to be closely related to acetaldehyde. An investigation of the modelled process dynamics in a continuous cultivation revealed multiple steady states in a region of dilution rates around the transition between oxidative and oxido-reductive growth. A bifurcation analysis using the two external variables, the dilution rate, D, and the inlet concentration of glucose, S(f), as parameters, showed that a fold bifurcation occurs close to the critical dilution rate resulting in multiple steady-states. The region of dilution rates within which multiple steady states may occur depends strongly on the substrate feed concentration. Consequently a single steady state may prevail at low feed concentrations, whereas multiple steady states may occur over a relatively wide range of dilution rates at higher feed concentrations.     

A structured growth model for Cynara cardunculus cell suspension

In this study a model was developed to describe the growth of Cynara cardunculus L. suspended cells as a function of the availability of two substrates, sucrose as the carbon and energy source and phosphate. It was assumed that the maintenance energy need was fulfilled by the consumption of extracellular carbohydrates, in non-limiting conditions, or by the consumption of structural biomass when sucrose is depleted. A production of secondary metabolites was also assumed. This model was developed based on a structured model previously described by Van Gulik et al. (1993). The model was applied to the experimental results of C. cardunculus suspended cells grown in a Gamborg B₅ medium supplemented with 2% sucrose, using a non-linear regression program.