重组毕赤酵母产青霉素G酰化酶的分批发酵动力学研究

构建了重组毕赤酵母产青霉素G酰化酶的分批发酵动力学模型。实验考察了分批发酵过程中甘油消耗、甲醇浓度、菌体浓度、溶氧、补料时间对青霉素G酰化酶活力的影响。应用Matlab软件,对菌体生长、基质消耗和产物生成方程进行最优参数估算和非线性拟合,得到相应的动力学模型。模型的计算值与实验值能较好地拟合,表明所建模型能较好反映重组毕赤酵母产青霉素G酰化酶的分批发酵过程。     

Identifiability and retrievability of unique parameters describing intrinsic Andrews kinetics

A key factor contributing to the variability in the microbial kinetic parameters reported from batch assays is parameter identifiability, i.e., the ability of the mathematical routine used for parameter estimation to provide unique estimates of the individual parameter values. This work encompassed a three-part evaluation of the parameter identifiability of intrinsic kinetic parameters describing the Andrews growth model that are obtained from batch assays. First, a parameter identifiability analysis was conducted by visually inspecting the sensitivity equations for the Andrews growth model. Second, the practical retrievability of the parameters in the presence of experimental error was evaluated for the parameter estimation routine used. Third, the results of these analyses were tested using an example data set from the literature for a self-inhibitory substrate. The general trends from these analyses were consistent and indicated that it is very difficult, if not impossible, to simultaneously obtain a unique set of estimates of intrinsic kinetic parameters for the Andrews growth model using data from a single batch experiment.     

Structured modeling and state estimation in a fermentation process: Lipase production by Candida rugosa

A simple structured mathematical model coupled with a methodology of state and parameter estimation is developed for lipase production by Candida rugosa in batch fermentation. The model describes the system according to the following qualitative observations and hypothesis: Lipase production is induced by extracellular oleic acid present in the medium. The acid is transported into the cell where it is consumed, transformed, and stored. Lipase is excreted to the medium where it is distributed between the available oil-water interphase and aqueous phase. Cell growth is modulated by the intracellular substrate concentration. Model parameters have been determined and the whole model validated against experiments not used in their determination. The estimation problem consists in the estimation of three state variables (biomass, intra- and extracellular substrate) and two kinetic parameters by using only the on-line measurement provided by exhaust gas analysis. The presented estimation strategy divides the complex problem into three subproblems that can be solved by stable algorithms. The estimation of biomass (X) and the specific growth rate (mu), is achieved by a recursive prediction error algorithm using the on-line measurement of the carbon dioxide evolution rate. mu is then used to perform an estimation of intracellular substrate and the other kinetic parameter related to substrate transport (A) by an adaptive observer. Extracellular substrate is then evaluated by means of the estimated values of intracellular substrate and biomass through the material balance of the reactor. Simulation and experimental tests showed good performance of the developed estimator, which appears suitable to be used for process control and monitoring. (c) 1995 John Wiley & Sons, Inc.     

产弹性蛋白酶细菌的发酵动力学研究

基于14L的发酵罐分批发酵实验数据,建立了发酵过程菌体生长、产物生成及基质消耗随时间变化的数学模型。Logistic方程、Luedeking—Piret方程能够很好地分别描述产弹性蛋白酶菌体生长;发酵产酶过程和基质消耗过程。并将3个动力学模型的预测值和实验值进行了比较,所建立的分批发酵动力学模型能较好地反映弹性蛋白酶分批发酵过程。     

Optimal fed batch experiment design for estimation of monod kinetics of Azospirillum brasilense: from theory to practice

In this paper the problem of reliable and accurate parameter estimation for unstructured models is considered. It is illustrated how a theoretically optimal design can be successfully translated into a practically feasible, robust, and informative experiment. The well-known parameter estimation problem of Monod kinetic parameters is used as a vehicle to illustrate our approach. As known for a long time, noisy batch measurements do not allow for unique and accurate estimation of the kinetic parameters of the Monod model. Techniques of optimal experiment design are, therefore, exploited to design informative experiments and to improve the parameter estimation accuracy. During the design process, practical feasibility has to be kept in mind. The designed experiments are easy to implement in practice and do not require additional monitoring equipment. Both design and experimental validation of informative fed batch experiments are illustrated with a case study, namely, the growth of the nitrogen-fixing bacteria Azospirillum brasilense.     

Mechanistic kinetic model for symmetric carboligations using benzaldehyde lyase

For reactions using thiamine diphosphate (ThDP)-dependent enzymes many empirically-derived kinetic models exist. However, there is a lack of mechanistic kinetic models. This is especially true for the synthesis of symmetric 2-hydroxy ketones from two identical aldehydes, with one substrate acting as the donor and the other as the acceptor. In this contribution, a systematic approach for deriving such a kinetic model for thiamine diphosphate (ThDP)-dependent enzymes is presented. The derived mechanistic kinetic model takes this donor-acceptor principle into account by containing two K(m)-values even for identical substrate molecules. As example the stereoselective carbon-carbon coupling of two 3,5-dimethoxy-benzaldehyde molecules to (R)-3,3',5,5'-tetramethoxy-benzoin using benzaldehyde lyase (EC 4.1.2.38) from Pseudomonas fluorescens is studied. The model is derived using a model-based experimental analysis method which includes parameter estimation, model analysis, optimal experimental design, in silico experiments, sensitivity analysis and model revision. It is shown that this approach leads to a robust kinetic model with accurate parameter estimates and an excellent prediction capability.     

Kinetic analysis of enzymatic chiral resolution by progress curve evaluation

The present study deals with kinetic modeling of enzyme-catalyzed reactions by integral progress curve analysis, and shows how to apply this technique to kinetic resolution of enantiomers. It is shown that kinetic parameters for both enantiomers and the enantioselectivity of the enzyme may be obtained from the progress curve measurement of a racemate only.A parameter estimation procedure has been established and it is shown that the covariance matrix of the obtained parameters is a useful statistical tool in the selection and verification of the model structure. Standard deviations calculated from this matrix have shown that progress curve analysis yields parameter values with high accuracies.Potential sources of systematic errors in (multiple) progress curve analysis are addressed in this article. Amongst these, the following needed to be dealt with: (1) the true initial substrate concentrations were obtained from the final amount of product experimentally measured (mass balancing); (2) systematic errors in the initial enzyme concentration were corrected by incorporating this variable in the fitting procedure as an extra parameter per curve; and (3) enzyme inactivation is included in the model and a first-order inactivation constant is determined.Experimental verification was carried out by continuous monitoring of the hydrolysis of ethyl 2-chloropropionate by carboxylesterase NP and the alpha-chymotrypsin-catalyzed hydrolysis of benzoylalanine mathyl ester in a pH-stat system. Kinetic parameter values were obtained with high accuracies and model predictions were in good agreement with independent measurements of enantiomeric excess values or literature data. (c) 1994 John Wiley & Sons, Inc.     

Modeling of single-cell oil production under nitrogen-limited and substrate inhibition conditions

Sweet sorghum extract was used as substrate for lipid accumulation by the oleaginous fungus Mortierella isabellina in batch cultures. Various initial sugar (13–91 g/L) and nitrogen (100–785 mg/L) concentrations resulting in various C/N (43–53) ratios were tested. Oil accumulation ranged between 43% and 51% corresponding to oil production from 2.2 to 9.3 g/L. A detailed mathematical model was developed. This model is able to adequately predict biomass growth, lipid accumulation, and sugar and nitrogen consumption. The model assumes that fungus growth is inhibited at high sugar concentrations. A set of kinetic experiments was used for model kinetic parameters estimation, while another set of experiments was used for model validation. The developed model could be generalized for similar systems of lipid accumulation and become a useful tool for reactor design for biofuel production. Bioeng. 2011; 108:1049–1055. © 2010 Wiley Periodicals, Inc.     

Least-squares estimation of batch culture kinetic parameters

This article concerns the development of a simple and effective least-squares procedure for estimating the kinetic parameters in Monod expressions from batch culture data. The basic approach employed in this work was to translate the problem of parameter estimation to a mathematical model containing a single decision variable. The resulting model was then solved by an efficient one-dimensional search algorithm which can be adapted to any microcomputer or advanced programmable calculator. The procedure was tested on synthetic data (substrate concentrations) with different types and levels of error. The effect of endogeneous respiration on the estimated values of the kinetic parameters was also assessed. From the results of these analyses the least-squares procedure developed was concluded to be very effective.     

Empirical modeling of batch fermentation kinetics for poly(glutamic acid) production and other microbial biopolymers

An empirical kinetic model is proposed for the batch production of poly(glutamic acid) from Bacillus subtilis IFO 3335. In addition, the proposed model was used to fit the kinetic data of poly(glutamic acid) production from other bacterial strains using different media, as well as kinetic data from different strains for the production of the exocellular biopolymers dextran, hyaluronic acid, xanthan, alginate, and the endocellular biopolymer polyhydroxybutyrate. The empirical model treats the biopolymer as a component of the biomass and fits the experimental biomass data using a sigmoidal relationship that includes the maximum specific growth rate, mu(max), and the substrate saturation parameter, K(S). An empirical parameter, the relative coefficient (r), quantifies, in relative terms, the degree of nongrowth-associated biopolymer formation.     

Mechanistic modeling of biodiesel production using a liquid lipase formulation

In this article, a kinetic model for the enzymatic transesterification of rapeseed oil with methanol using Callera? Trans L (a liquid formulation of a modified Thermomyces lanuginosus lipase) was developed from first principles. We base the model formulation on a Ping‐Pong Bi‐Bi mechanism. Methanol inhibition, along with the interfacial and bulk concentrations of the enzyme was also modeled. The model was developed to describe the effect of different oil compositions, as well as different water, enzyme, and methanol concentrations, which are relevant conditions needed for process evaluation, with respect to the industrial production of biodiesel. The developed kinetic model, coupled with a mass balance of the system, was fitted to and validated on experimental results for the fed‐batch transesterification of rapeseed oil. The confidence intervals of the parameter estimates, along with the identifiability of the model parameters were presented. The predictive capability of the model was tested for a case using 0.5% (wt. Enzyme/wt. Oil), 0.5% (wt. Water /wt. Oil) and feeding 1.5 times the stoichiometric amount of methanol in total over 24 h. For this case, an optimized methanol feeding profile that constrains the amount of methanol in the reactor was computed and the predictions experimentally validated. Monte‐Carlo simulations were then used to characterize the effect of the parameter uncertainty on the model outputs, giving a biodiesel yield, based on the mass of oil, of 90.8 ± 0.55 mass %. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 30:1277–1290, 2014     

A robust methodology for kinetic model parameter estimation for biocatalytic reactions

Effective estimation of parameters in biocatalytic reaction kinetic expressions are very important when building process models to enable evaluation of process technology options and alternative biocatalysts. The kinetic models used to describe enzyme‐catalyzed reactions generally include several parameters, which are strongly correlated with each other. State‐of‐the‐art methodologies such as nonlinear regression (using progress curves) or graphical analysis (using initial rate data, for example, the Lineweaver‐Burke plot, Hanes plot or Dixon plot) often incorporate errors in the estimates and rarely lead to globally optimized parameter values. In this article, a robust methodology to estimate parameters for biocatalytic reaction kinetic expressions is proposed. The methodology determines the parameters in a systematic manner by exploiting the best features of several of the current approaches. The parameter estimation problem is decomposed into five hierarchical steps, where the solution of each of the steps becomes the input for the subsequent step to achieve the final model with the corresponding regressed parameters. The model is further used for validating its performance and determining the correlation of the parameters. The final model with the fitted parameters is able to describe both initial rate and dynamic experiments. Application of the methodology is illustrated with a case study using the ω‐transaminase catalyzed synthesis of 1‐phenylethylamine from acetophenone and 2‐propylamine. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

Re-interpretation of the logistic equation for batch microbial growth in relation to Monod kinetics

Aims:  To determine the underlying substrate utilization mechanism in the logistic equation for batch microbial growth by revealing the relationship between the logistic and Monod kinetics. Also, to determine the logistic rate constant in terms of Monod kinetic constants.
Methods and Results:  The logistic equation used to describe batch microbial growth was related to the Monod kinetics and found to be first-order in terms of the substrate and biomass concentrations. The logistic equation constant was also related to the Monod kinetic constants. Similarly, the substrate utilization kinetic equations were derived by using the logistic growth equation and related to the Monod kinetics.
Conclusion:  It is revaled that the logistic growth equation is a special form of the Monod growth kinetics when substrate limitation is first-order with respect to the substrate concentration. The logistic rate constant ( k ) is directly proportional to the maximum specific growth rate constant ( μ _m) and initial substrate concentration ( S ₀) and also inversely related to the saturation constant ( K _s).
Significance and Impact of the Study:  The semi-empirical logistic equation can be used instead of Monod kinetics at low substrate concentrations to describe batch microbial growth using the relationship between the logistic rate constant and the Monod kinetic constants.     

Analysis of the quasi-steady-state approximation for an enzymatic one-substrate reaction

The validity of the quasi-steady state approximation for the calculation of the rate function of an isolated enzyme reaction is analysed by a detailed consideration of the time dependent process. For the characterization of the deviations of the real motion from the quasi-stationary state three kinds of error functions are used, the relaxation deficit, the relative relaxation time and the relaxation error. An improved approximation procedure is developed to calculate the transient states of the system. The maximum distance of the original motion from the quasi-stationary states is estimated by a general method. By consideration of different enzyme and substrate concentrations as well as different kinetic constants those parameter regions have been determined, where the errors of the quasi-steady state approximation do not exceed tolerated values. It is suggested how the methods can be applied to metabolic pathways.     

A kinetic study of lipase-catalyzed reversible kinetic resolution involving verification at miniplant-scale

Lipase-catalyzed kinetic resolution of racemates is a popular method for synthesis of chiral synthons. Most of these resolutions are reversible equilibrium limited reactions. For the first time, an extensive kinetic model is proposed for kinetic resolution reactions, which takes into account the full reversibility of the reaction, substrate inhibition by an acyl donor and an acyl acceptor as well as alternative substrate inhibition by each enantiomer. For this purpose, the reversible enantioselective transesterification of (R/S)-1-methoxy-2-propanol with ethyl acetate catalyzed by Candida antarctica lipase B (CAL-B) is investigated. The detailed model presented here is valid for a wide range of substrate and product concentrations. Following model discrimination and the application of Haldane equations to reduce the degree of freedom in parameter estimation, the 11 free parameters are successfully identified. All parameters are fitted to the complete data set simultaneously. Six types of independent initial rate studies provide a solid data basis for the model. The effect of changes in substrate and product concentration on reaction kinetics is discussed. The developed model is used for simulations to study the behavior of reaction kinetics in a fixed bed reactor. The typical plot of enantiomeric excess versus conversion of substrate and product is evaluated at various initial substrate mixtures. The model is validated by comparison with experimental results obtained with a fixed bed reactor, which is part of a fully automated state-of-the-art miniplant.     

法夫酵母分批发酵虾青素动力学研究

通过三联30L全自动发酵罐对虾青素产生菌法夫酵母的分批发酵动力学进行了研究,结果表明,法夫酵母的生长与限制性基质葡萄糖浓度之间符合Logistic方程,建立了细胞生长、产物合成和基质消耗随时间变化的数学模型。应用MATLAB软件对发酵动力学模型进行最优参数估计和非线性拟和,获得最大比生长速率（umax）和产物得率（Yp/x）分别为0.1829/h、0.1524g/g,虾青素分批发酵中细胞生长与产物合成属于偶联型,模型模拟计算结果和实验值能较好地吻合,动力学研究结果表明该模型能较好地反映细胞的生长、底物消耗和产物合成过程机制。     

Co-immobilization of dextransucrase and dextranase for the facilitated synthesis of isomalto-oligosaccharides: Preparation, characterization and modeling

Co-Immobilization of dextransucrase (DS) and dextranase (DN) into calcium alginate includes the co-entrapment of soluble DS and adsorbed DN. DS converts sucrose into dextran, which is the substrate for DN, so that isomalto-oligosaccharides (IMOs) are follow-up products of dextran hydrolysis. The boundary conditions for the successful preparation are investigated with respect to choice of DN adsorbate, surface modifications using blotting agents and optimal enzyme activity ratios. Further, repetitive batch experiments suggest the selection of medium activity ratios for continuous use (0.3 U(DN)U(-1) (DS), e.g.). Product formation at various cosubstrate:substrate concentrations as well as at different DN:DS ratios are discussed. Moreover, the complexity of the bi-enzymatic system can be reduced considering the molar ratios of cosubstrate:substrate (glucose:sucrose). Based on these factors, a mechanistic kinetic model is developed, which distinguishes the corresponding contributions of the two enzymes upon overall product formation. In general, at low glucose:sucrose ratios isomaltose synthesis is featured primarily by DN action. Yet with increasing amounts of glucose both the quantity and quality of DN substrate changes, so that its contribution to product formation decreases in an exponential manner; still the overall product yield continuously increases due to enhanced DS contribution.     

Some examples of the use of computer-produced contour plots in the fitting of enzyme rate equations to reaction-velocity measurements

The use of computer-based isotach plots, relating reaction velocity to simultaneous variation of two substrates or effectors of an enzyme, in producing estimates of the parameters of enzyme rate equations was investigated. The computer program (;SYMAP') incorporates an interpolation algorithm, and the superiority of this over visual estimation in producing interpolated velocity values for the estimation of parameter values by conventional double-reciprocal plots is described. The usefulness of the SYMAP program in monitoring the process of fitting data obtained by simultaneous changes in two experimental variables is also described. It is shown that if the residual errors are weighted by a procedure described elsewhere (Ottaway, 1971b, 1973), the percentage error of the computed velocity is distributed evenly over a plot which contains a 100-fold variation in the concentration of one substrate and a 500-fold variation in the concentration of Mg(2+), and in which the velocity of the reaction (that catalysed by NAD kinase) varies over a 60-fold range. The two-dimensional percentage error plot was used to assess the limits within which an incomplete inhibition equation is valid, and to detect a discrepancy in an expected good fit, caused by an impurity in one of the substrates.     

Biocatalytic process optimization based on mechanistic modeling of cholic acid oxidation with cofactor regeneration

Reduction and oxidation of steroids in the human gut are catalyzed by hydroxysteroid dehydrogenases of microorganisms. For the production of 12-ketochenodeoxycholic acid (12-Keto-CDCA) from cholic acid the biocatalytic application of the 12α-hydroxysteroid dehydrogenase of Clostridium group P, strain C 48-50 (HSDH) is an alternative to chemical synthesis. However, due to the intensive costs the necessary cofactor (NADP(+) ) has to be regenerated. The alcohol dehydrogenase of Thermoanaerobacter ethanolicus (ADH-TE) was applied to catalyze the reduction of acetone while regenerating NADP(+) . A mechanistic kinetic model was developed for the process development of cholic acid oxidation using HSDH and ADH-TE. The process model was derived by identifying the parameters for both enzymatic models separately using progress curve measurements of batch processes over a broad range of concentrations and considering the underlying ordered bi-bi mechanism. Both independently derived kinetic models were coupled via mass balances to predict the production of 12-Keto-CDCA with HSDH and integrated cofactor regeneration with ADH-TE and acetone as co-substrate. The prediction of the derived model was suitable to describe the dynamics of the preparative 12-Keto-CDCA batch production with different initial reactant and enzyme concentrations. These datasets were used again for parameter identification. This led to a combined model which excellently described the reaction dynamics of biocatalytic batch processes over broad concentration ranges. Based on the identified process model batch process optimization was successfully performed in silico to minimize enzyme costs. By using 0.1 mM NADP(+) the HSDH concentration can be reduced to 3-4 μM and the ADH concentration to 0.4-0.6 μM to reach the maximal possible conversion of 100 mM cholic acid within 48 h. In conclusion, the identified mechanistic model offers a powerful tool for a cost-efficient process design.