Modeling and parameters identification of 2-keto-<Emphasis Type="SmallCaps">l</Emphasis>-gulonic acid fed-batch fermentation

This article presents a modeling approach for industrial 2-keto-l-gulonic acid (2-KGA) fed-batch fermentation by the mixed culture of Ketogulonicigenium vulgare (K. vulgare) and Bacillus megaterium (B. megaterium). A macrokinetic model of K. vulgare is constructed based on the simplified metabolic pathways. The reaction rates obtained from the macrokinetic model are then coupled into a bioreactor model such that the relationship between substrate feeding rates and the main state variables, e.g., the concentrations of the biomass, substrate and product, is constructed. A differential evolution algorithm using the Lozi map as the random number generator is utilized to perform the model parameters identification, with the industrial data of 2-KGA fed-batch fermentation. Validation results demonstrate that the model simulations of substrate and product concentrations are well in coincidence with the measurements. Furthermore, the model simulations of biomass concentrations reflect principally the growth kinetics of the two microbes in the mixed culture.     

Macrokinetic model for Gluconobacter oxydans in 2-keto-L-gulonic acid mixed culture

A set of kinetic models have been developed for the production of 2-keto-L-gulonic acid from L-sorbose by a mixed culture of Gluconobacter oxydans and Bacillus megaterium. A metabolic pathway is proposed for Gluconobacter oxydans, and a macrokinetic model has been developed for Gluconobacter oxydans, where the balances of some key metabolites, ATP and NADH are taken into account. An unstructured model is proposed for concomitant bacterium Bacillus megaterium. In the macrokinetic model and unstructured model, the mechanism of interaction between Gluconobacter oxydans and Bacillus megaterium is investigated and modeled. The specific substrate uptake rate and the specific growth rate obtained from the macrokinetic model are then coupled into a bioreactor model such that the relationship between the substrate feeding rate and the main state variables, such as the medium volume, the biomass concentrations, the substrate, and the is set up. A closed loop regulator model is introduced to approximate the induction of enzyme pool during lag phase after inoculation. Experimental results demonstrate that the model is able to describe 2-keto-L-gulonic acid fermentation process with reasonable accuracy.     

Cybernetic modeling based on pathway analysis for Penicillium chrysogenum fed-batch fermentation

A macrokinetic model employing cybernetic methodology is proposed to describe mycelium growth and penicillin production. Based on the primordial and complete metabolic network of Penicillium chrysogenum found in the literature, the modeling procedure is guided by metabolic flux analysis and cybernetic modeling framework. The abstracted cybernetic model describes the transients of the consumption rates of the substrates, the assimilation rates of intermediates, the biomass growth rate, as well as the penicillin formation rate. Combined with the bioreactor model, these reaction rates are linked with the most important state variables, i.e., mycelium, substrate and product concentrations. Simplex method is used to estimate the sensitive parameters of the model. Finally, validation of the model is carried out with 20 batches of industrial-scale penicillin cultivation.     

Macrokinetic model for methylotrophic Pichia pastoris based on stoichiometric balance

A macrokinetic model for Pichia pastoris expressing recombinant human serum albumin is proposed. The model describes the balances of some key metabolites, ATP and NADH, during glycerol and methanol metabolism. In the glycerol growth phase, the metabolic pathways mainly include phosphorylation, glycolysis, tricarboxylic acid cycle, and respiratory chain. In the methanol growth phase, methanol is oxidized to formaldehyde at first. Then, while a part of formaldehyde is oxidized to formate, the rest is condensed with xylulose-5-monophosphate to form glyceraldehyde-3-phosphate, and further assimilated to form cell constituents. The metabolic pathways following glyceraldehyde-3-phosphate were assumed to be similar to those in the glycerol growth phase. Based on the model, the macrokinetic bioreaction rates such as the specific substrate consumption rate, the specific growth rate, the specific acetyl-CoA formation rate as well as the specific oxygen uptake rate are obtained. The specific substrate consumption rate and the specific growth rate are then coupled into a bioreactor model such that the relationship between substrate feeding rates and the main state variables, i.e., the medium volume, the concentrations of the biomass, the substrate, and the product, is set up. Experimental results demonstrate that the model can describe the cell growth and the protein production with reasonable accuracy.     

Cell cycle model for recombinant Pichia pastoris during glycerol fed-batch cultivation

A cell cycle model is proposed for methylotrophic yeast Pichia pastoris grown on glycerol during fed-batch cultivation. Morphological differentiation of cells, such as unbudded daughter cell, unbudded parent cell and budding cell, is depicted by the model. During the cyclic growth, cells in different cycling period are assumed to undergo sequential shifting dominantly. The input of the cell cycle model is the specific growth rate, which is calculated from the macrokinetic model proposed previously. The cell cycle related variables, such as the fraction of budding cells and the cell density are then simulated. Model validation is carried out with the experimental data of off-line assays.     

A theoretical study of concentration of profiles of primary cytochemical-enzyme reaction products in membrane-bound cell organelles and its application to lysosomal acid phosphatase

Synopsis A numerical method was developed for computing the steady-state concentration gradient of a diffusible enzyme reaction product in a membrane-limited compartment of a simplified theoretical cell model. In cytochemical enzyme reactions proceeding according to the metal-capture principle, the local concentration of the primary reaction product is an important factor in the onset of the precipitation process and in the distribution of the final reaction product. The following variables were incorporated into the model: enzyme activity, substrate concentration,K _m, diffusion coefficient of substrate and product, particle radius and cell radius.The method was applied to lysosomal acid phosphatase. Numerical values for the variables were estimated from experimental data in the literature. The results show that the calculated phosphate concentrations inside lysosomes are several orders of magnitude lower than the critical concentrations for efficient phosphate capture found in a previous experimental model study. Reasons for this apparent discrepancy are discussed.     

Application of an extended kalman filter method for monitoring high density cultivation of Escherichia coli

A real-time, on-line extended Kalman filter was used to describe and monitor the growth of Escherichia coli on glycerol. The growth of E. coli showed an inhibition kinetics with μ_max=0.806/h, K_S=0.68 g/l and K_i=87.4 g/l. As a feeding strategy, the conventional DO-stat with a DDC-PID control method, in which the dissolved oxygen concentration is maintained at a desired level by varying the substrate feedrate, was employed. The Kalman filter was based on an unstructured mathematical model and on-line measured data. The mathematical model comprised of mass balances of the biomass and substrate as well as kinetic and stoichiometric data which were measured prior to the process. For biomass concentration up to 50 g dry weight/l, the estimation of the process was rather accurate. At higher biomass concentration, product formation, indicated by an intense brown coloring of the fermentation broth, occured. Since the effect of this product on biomass production was not included in the mathematical model, the estimated data diverged from the experimental data at biomass concentrations greater than 50 g dry weight/l.     

Identification of unstructured model for subtilin production through Bacillus subtilis using hybrid genetic algorithm

Subtilin production is favorable when Bacillus subtilis 168 is subjected to stress condition such as nutrient scarcity. A mathematical model underlying such growth process has immense applicability in determining the optimal operating conditions at industrial scale. We present this work with multiple objectives of a) selection of a substrate for creating the minimal nutrient media for B. subtilis thereby enhancing subtilin production, b) experimental study of the growth along with morphological characteristics of B. subtilis and product profile in nutrient scarcity condition and c) identification of an optimal unstructured model for subtilin production using a computational framework. First, we show that subtilin can be produced while B. subtilis is grown using galactose and B. subtilis undergoes morphological changes and takes filamentous shape. We then constructed a series of plausible models and used a hybrid method combining Genetic Algorithm and gradient based search methodologies, for model selection. The estimated kinetic parameters and the stoichiometric analysis indicate that the B. subtilis growth/death, product profile and respiratory mechanism undergo specific modifications in galactose as an adaptive response. Current study provides an inexpensive platform to produce subtilin and the predictive framework presented here has potential applications for large scale production of subtilin.     

A rapid assay for epoxide hydratase activity with benzo(a)pyrene 4,5-(K-region-)oxide as substrate

A rapid radiometric assay for epoxide hydratase activity has been developed using the highly mutagenic [³H]benzo(a)pyrene 4,5-(K-region-)oxide as substrate. By addition of dimethylsulfoxide after the incubation, conditions were found where the unreacted substrate could be separated from the product benzo(a)pyrene-4,5-dihydrodiol(trans) simply by extraction into petroleum ether. The product is then extracted into ethyl acetate and, radioactivity is measured by scintillation spectrometry. This assay allows a rapid measurement of epoxide hydratase activity with an epoxide derived from a carcinogenic polycyclic hydrocarbon as substrate and is at the same time sensitive enough for accurate determination of epoxide hydratase activity in preparations with extremely low enzyme levels such as rat skin homogenate (8–14 pmol of product/mg of protein/min).     

Displacement of a DNA binding protein by Dda helicase

Bacteriophage T4 Dda helicase has recently been shown to be active as a monomer for unwinding of short duplex oligonucleotides and for displacing streptavidin from 3′-biotinylated oligonucleotides. However, its activity for streptavidin displacement and DNA unwinding has been shown to increase as the number of Dda molecules bound to the substrate molecule increases. A substrate was designed to address the ability of Dda to displace DNA binding proteins. A DNA binding site for the Escherichia coli trp repressor was introduced into an oligonucleotide substrate for Dda helicase containing single-stranded overhang. Here we show that a Dda monomer is insufficient to displace the E.coli trp repressor from dsDNA under single turnover conditions, although the substrate is unwound and the repressor displaced when the single-stranded overhang is long enough to accommodate two Dda molecules. The quantity of product formed increases when the substrate is able to accommodate more than two Dda molecules. These results indicate that multiple Dda molecules act to displace DNA binding proteins in a manner that correlates with the DNA unwinding activity and streptavidin displacement activity. We suggest a cooperative inchworm model to describe the activities of Dda helicase.     

Effects of high product and substrate inhibitions on the kinetics and biomass and product yields during ethanol batch fermentation

In ethanol fermentation, instantaneous biomass yield of the yeast Saccharmoyces cerevisiae was found to decrease (from 0.156 to 0.026) with increase in ethanol concentration (from 0 to 107 g/L), indicating a definite relationship between biomass yield and product inhibition. A suitable model was proposed to describe this decrease which incorporates the kinetic parameters of product inhibition rather than pure empirical constants. Substrate inhibition was found to occur when substrate concentration is above 150 g/L. A similar definite relationship was observed between substrate inhibition and instantaneous biomass yield. A simple empirical model is proposed to describe the declines in specfic growth rate and biomass yield due to substrate inhibition. It is observed that product inhibition does not have any effect on product yield whereas substrate inhibition significantly affects the product yield, reflecting a drop in overall product yield from 0.45 to 0.30 as the initial substrate concentration increases from 150 to 280 g/L. These results are expected to have a significant influence in formulating optimum fermentor design variables and in developing an effective control strategy for optimizing ethanol producitivity.     

Experimental design for the identification of macrokinetic models and model discrimination

An experimental design method for the identification of macrokinetic models was developed applying an extended D-optimal design criterion. The D-optimal design criterion was modified to consider variable measurement variances as well as multivariate macrokinetic models. The macrokinetics of formate dehydrogenase (FDH) production with Candida boidinii were thus identified within 10 steady state experiments in a labscale continuous stirred tank reactor (10 model parameters). Closed loop control (nutristat) was applied to set-up the operating states suggested by this experimental design method. After each set of steady state experiments the quality of macrokinetic parameters was characterized statistically. For model discrimination a parameter discrimination algorithm based on entropy formulations was adapted. Again a multivariate criterion considering variable measurement variances was developed. This discrimination algorithm was applied to discriminate the macrokinetic model of FDH production with Candida boidinii out of 10 different macrokinetic approaches. An unequivocal discrimination result could be obtained calculating model specific probabilities. These were compared with commonly used sum of squares values. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 564-576, 1997.     

A simultaneous saccharification and fermentation model for dynamic growth environments

Many mathematical models by researchers have been formulated for Saccharomyces cerevisiae which is the common yeast strain used in modern distilleries. A cybernetic model that can account for varying concentrations of glucose, ethanol and organic acids on yeast cell growth dynamics does not exist. A cybernetic model, consisting of 4 reactions and 11 metabolites simulating yeast metabolism, was developed. The effects of variables such as temperature, pH, organic acids, initial inoculum levels and initial glucose concentration were incorporated into the model. Further, substrate and product inhibitions were included. The model simulations over a range of variables agreed with hypothesized trends and to observations from other researchers. Simulations converged to expected results and exhibited continuity in predictions for all ranges of variables simulated. The cybernetic model did not exhibit instability under any conditions simulated.     

Product inhibition studies and the reaction sequence of rabbit adrenal norepinephrine N-methyl transferase isozymes

The effects of reaction products on the steady-state kinetic properties of the five charge isozymes of rabbit adrenal norepinephrine N-methyl transferase have been investigated. Qualitative and quantitative differences were observed for the isozymes. The only characteristic that was common to all isozymes was the competition between S-adenosylmethionine and S-adenosylhomocysteine for the binding site. In most instances, the product inhibition constants were sufficiently low to suggest that product inhibition may be an important factor in regulating the activities of the isozymes. A reaction model is proposed for rabbit adrenal norepinephrine N-methyl transferase which is consistent with results observed in investigations of the steady-state kinetic properties of the five charge isozymes. The proposed model is that of an ordered sequential reaction sequence in which the active center contains a binding site for S-adenosylmethionine and S-adenosylhomocysteine, and a binding site for norepinephrine and epinephrine. The proposed model includes the formation of a number of abortive complexes between enzyme and substrate and product, but not all of the abortive complexes are significant kinetically in the case of some of the isozymes. The differences in the steady-state kinetic characteristics of the isozymes are attributed to differences in the magnitudes of the rate constants of some of the individual steps.     

Engineering cytosolic acetyl-coenzyme A supply in Saccharomyces cerevisiae: Pathway stoichiometry,free-energy conservation and redox-cofactor balancing

Saccharomyces cerevisiae is an important industrial cell factory and an attractive experimental model for evaluating novel metabolic engineering strategies. Many current and potential products of this yeast require acetyl coenzyme A (acetyl-CoA) as a precursor and pathways towards these products are generally expressed in its cytosol. The native S. cerevisiae pathway for production of cytosolic acetyl-CoA consumes 2 ATP equivalents in the acetyl-CoA synthetase reaction. Catabolism of additional sugar substrate, which may be required to generate this ATP, negatively affects product yields. Here, we review alternative pathways that can be engineered into yeast to optimize supply of cytosolic acetyl-CoA as a precursor for product formation. Particular attention is paid to reaction stoichiometry, free-energy conservation and redox-cofactor balancing of alternative pathways for acetyl-CoA synthesis from glucose. A theoretical analysis of maximally attainable yields on glucose of four compounds (n-butanol, citric acid, palmitic acid and farnesene) showed a strong product dependency of the optimal pathway configuration for acetyl-CoA synthesis. Moreover, this analysis showed that combination of different acetyl-CoA production pathways may be required to achieve optimal product yields. This review underlines that an integral analysis of energy coupling and redox-cofactor balancing in precursor-supply and product-formation pathways is crucial for the design of efficient cell factories.     

An immobilized cell reactor with simultaneous product separation. I. Reactor design and analysis

A four-phase reactor-separator (gas, liquid, solid, and immobilized catalyst) is proposed for fermentations characterized by a volatile product and nonvolatile substrate.In this reactor, the biological catalyst is immobilized onto a solid column packing and contacted by the liquid containing the substrate.A gas phase is also moved through the column to strip the volatile product into the gas phase. The Immobilized Cell Reactor-Separator (ICRS) consists of two basic gas-liquid flow sections: a cocurrent "enricher" followed by a countercurrent-"stripper".In this article, an equilibrium stage model of the reactor is developed to determine the feasibility and important operational variables of such a reactor-separator. The ICRS concept is applied to the ethanol from whey lactose fermentation using some preliminary immobilized cell reactor performance data. A mathematical model for a steady-state population based on an adsorbed monolayer of cells is also developed for the reactor. The ICRS model demonstrated that the ICRS should give a significant increase in reactor productivity as compared to an identically sized Immobilized Cell Reactor (ICR) with no separation. The gas-phase separation of the product also allows fermentation of high inlet substrate concentrations. The model is used to determine the effects of reactor parameters on ICRS performance including temperature, pressure, gas flow rates, inlet substrate concentration, and degree of microbial product inhibition.     

The Reductive Half-reaction of Xanthine Dehydrogenase from Rhodobacter capsulatus: THE ROLE OF GLU232 IN CATALYSIS*

The kinetic properties of an E232Q variant of the xanthine dehydrogenase from Rhodobacter capsulatus have been examined to ascertain whether Glu²³² in wild-type enzyme is protonated or unprotonated in the course of catalysis at neutral pH. We find that k_red, the limiting rate constant for reduction at high [xanthine], is significantly compromised in the variant, a result that is inconsistent with Glu²³² being neutral in the active site of the wild-type enzyme. A comparison of the pH dependence of both k_red and k_red/K_d from reductive half-reaction experiments between wild-type and enzyme and the E232Q variant suggests that the ionized Glu²³² of wild-type enzyme plays an important role in catalysis by discriminating against the monoanionic form of substrate, effectively increasing the pK_a of substrate by two pH units and ensuring that at physiological pH the neutral form of substrate predominates in the Michaelis complex. A kinetic isotope study of the wild-type R. capsulatus enzyme indicates that, as previously determined for the bovine and chicken enzymes, product release is principally rate-limiting in catalysis. The disparity in rate constants for the chemical step of the reaction and product release, however, is not as great in the bacterial enzyme as compared with the vertebrate forms. The results indicate that the bacterial and bovine enzymes catalyze the chemical step of the reaction to the same degree and that the faster turnover observed with the bacterial enzyme is due to a faster rate constant for product release than is seen with the vertebrate enzyme.     

A highly sensitive and rapid fluorometric assay for UDP-glucuronyltransferase using 3-hydroxybenzo (a) pyrene as substrate.

A rapid and highly sensitive fluorometric assay for UDP-glucuronyltransferase (EC 2.4.1.17) has been devised using 3-hydroxybenzo(a)pyrene as substrate. The sensitivity of the procedure is based on (a) the high coefficient of fluorescence of the product, benzo(a)pyrene-3-glucuronide, and (b) the very low background which is obtained by an efficient differential extraction of substrate and product and their widely differing fluorescence characteristics in alkaline solution. As little as 5–10 pmol of product can be determined. The procedure involves essentially a single extraction and transfer step. The method may be applicable in measuring transferase activity in a few micrograms of tissue protein or of cultured cells as well as in the routine processing of large numbers of samples. Some of the properties of glucuronyltransferase activity directed toward 3-hydroxybenzo(a)pyrene are described such as kinetic constants and the sensitivity of the reaction to detergents and organic solvents.     

Chiral Hydroxylation at the Mononuclear Nonheme Fe(II) Center of 4-(S) Hydroxymandelate Synthase – A Structure-Activity Relationship Analysis

(S)-Hydroxymandelate synthase (Hms) is a nonheme Fe(II) dependent dioxygenase that catalyzes the oxidation of 4-hydroxyphenylpyruvate to (S)-4-hydroxymandelate by molecular oxygen. In this work, the substrate promiscuity of Hms is characterized in order to assess its potential for the biosynthesis of chiral α-hydroxy acids. Enzyme kinetic analyses, the characterization of product spectra, quantitative structure activity relationship (QSAR) analyses and in silico docking studies are used to characterize the impact of substrate properties on particular steps of catalysis. Hms is found to accept a range of α-oxo acids, whereby the presence of an aromatic substituent is crucial for efficient substrate turnover. A hydrophobic substrate binding pocket is identified as the likely determinant of substrate specificity. Upon introduction of a steric barrier, which is suspected to obstruct the accommodation of the aromatic ring in the hydrophobic pocket during the final hydroxylation step, the racemization of product is obtained. A steady state kinetic analysis reveals that the turnover number of Hms strongly correlates with substrate hydrophobicity. The analysis of product spectra demonstrates high regioselectivity of oxygenation and a strong coupling efficiency of C-C bond cleavage and subsequent hydroxylation for the tested substrates. Based on these findings the structural basis of enantioselectivity and enzymatic activity is discussed.     

Macrokinetic basis for the model of microbial growth in a limited volume under constant conditions with a single leading substrate

Within the framework of the macrokinetic approach and continuum and chemical/biochemical gross reaction conceptions, an equation describing the complete dynamics of microbial growth and decline as function of a variable concentration of the leading substrate was deduced. This equation allows us to distinguish quantitatively and qualitatively the stages of microbial growth and the intervals of microbial tolerance to the initial concentration of the leading substrate. Adequacy of the model was confirmed by comparison with experimental dynamics of aerobic microorganisms in the samples of groundwater collected from a region polluted with uranium.