Adaptive on-line model for aerobic Saccharomyces cerevisiae fermentation

In order to study and control fermentation processes, indirect on-tine measurements and mathematical models can be used. In this article we present a mathematical on-line model for fermentation processes. The model is based on atom and partial mass balances as well as on equations describing the acid-base system. The model is brought into an adaptive form by including transport equations for mass transfer and unstructured expressions for the fermentation kinetics. The state of the process, i.e., the concentrations of biomass, substrate, and products, can be estimated on-line using the balance part of the model completed with measurement equations for the input and output flows of the process. Adaptivity is realized by means of on-line estimation of parameters in the transport and kinetic expressions using recursive regression analysis. These expressions can thus be used in the model as valid equations enabling prediction of the process. This makes model-based automation of the process and testing of the validity of the measurement variables possible. The model and the on-line principles are applied to a 3.5-L laboratory tormentor in which Saccharomyces cerevisiae is cultivated. The experimental results show that the model-based estimation of the state and the predictions of the process correlate closely with high-performance liquid chromatography (HPLC) analyses. (c) 1995 John Wiley & Sons, Inc.     

State and parameter estimation of microalgal photobioreactor cultures based on local irradiance measurement

Local photosynthetic photon flux fluence rate (PPFFR) determined by a submersible 4pi quantum micro-sensor was used in developing a versatile on-line state estimator for stirred-tank microalgal photobioreactor cultures. A marine micro-alga Dunaliella salina was used as a model organism in this study. On-line state estimation was realized using the extended Kalman filter (EKF), based on a state model of the photobioreactor and on-line local PPFFR measurement. The dynamic state model for the photobioreactor was derived based on mass-balance equations of the relevant states. The measurement equation was established based on an empirical correlation between the microalgal biomass concentration and the local PPFFR measured at a fixed point inside the photobioreactor. An internal model approach was used to estimate the specific growth rate without the need of state-based kinetic expression. The estimator was proven to be capable of estimating biomass concentration and specific growth rate, as well as phosphate and dissolved oxygen concentrations in a photobioreactor illuminated with either fixed or time-varying incident radiation. The quantum sensor was shown to be robust and able to quickly respond to dynamic changes in local PPFFR. In addition, the quantum sensor outputs were not affected by bubble aeration or agitation within the typical operating range. The strong filtering capacity of EKF gives the state estimator superior performance compared to direct calculation from the empirical biomass/local PPFFR correlation. This state estimation system makes use of inexpensive and reliable sensor hardware to report key process dynamics of microalgal photobioreactor cultures on-line, enabling improved operation of such a process.     

Experimental design for optimal parameter estimation of an enzyme kinetic process based on the analysis of the Fisher information matrix

The investigation of enzyme kinetics is increasingly important, especially for finding active substances and understanding intracellular behaviors. Therefore, the determination of an enzyme's kinetic parameters is crucial. For this a systematic experimental design procedure is necessary to avoid wasting time and resources. The parameter estimation error of a Michaelis-Menten enzyme kinetic process is analysed analytically to reduce the search area as well as numerically to specify the optimum for parameter estimation. From analytical analysis of the Fisher information matrix the fact is obtained, that an enzyme feed will not improve the estimation process, but substrate feeding is favorable with small volume flow. Unconstrained and constrained process conditions are considered. If substrate fed-batch process design is used instead of pure batch experiments the improvements of the Cramer-Rao lower bound of the variance of parameter estimation error reduces to 82% for mu(max) and to 60% for K(m) of the batch values in average.     

Modeling lipid accumulation and degradation in Yarrowia lipolytica cultivated on industrial fats

A modeling approach was used to quantify the kinetic behavior of a Yarrowia lipolytica strain capable of producing significant lipid amounts when cultivated on industrial fats. Biomass and cellular lipid evolution were successfully simulated, while the optimized parameter values were similar to those experimentally measured. The maximum specific formation rate of fat-free biomass seemed unaffected by the substrate fatty acid composition. On the contrary, the maximum concentration of lipid accumulated inside the yeast cell, as well as the maximum specific accumulation rate of cellular lipids, was favored in high stearic acid content media. The microorganism presented the tendency to degrade its accumulated lipids, although remarkable substrate fat amounts remained unconsummated in the culture medium. This degradation slowly occurred in the yeast cell as the specific rate of the intracellular carbon pool (storage lipid consumption) was significantly lower compared with that of the extracellular carbon pool (substrate fat). However, the fat-free biomass yield on storage lipids (g of fat-free biomass formed per g of storage lipids consumed) was higher than the one on the substrate (g of fat-free biomass formed per g of medium fat consumed).     

On-line monitoring of PHB production by mixed microbial cultures using respirometry,titrimetry and chemometric modelling

This work describes a method for on-line monitoring of biomass production, acetate consumption and intracellular polyhydroxybutyrate (PHB) storage by mixed microbial cultures (MMC). The method is based on reliable and easily available on-line measurements, namely pH, dissolved oxygen, dissolved carbon dioxide, on-line respirometry and on-line titrimetric analysis. Biomass production refers to active biomass growth and also to the synthesis of extracellular polymeric substances (EPS). The composition and kinetics of EPS synthesis has high variability depending on the culture enrichment protocol. Since the metabolism for EPS production is rather difficult to define, it was not possible to develop a reliable estimation model based on metabolic principles only. Instead, projection of latent structures (PLS) linear regression constrained by steady state carbon balance was employed. PHB concentration and biomass production rate were directly estimated by the PLS model, whereas acetate concentration was indirectly estimated through the carbon balance. The method was validated experimentally with data of four experiments carried out in a SBR. Accurate on-line estimations were obtained with regression coefficients (r²) of 0.986 and 0.980 for biomass concentration, 0.976 and 0.999 for PHB and 0.992 and 0.999 for acetate concentration in calibration and validation, respectively. These results confirm the ability of the proposed methodology for on-line monitoring of the state variables in PHB production process by MMC.     

Modeling Lipid Accumulation and Degradation in Yarrowia lipolytica Cultivated on Industrial Fats

A modeling approach was used to quantify the kinetic behavior of a Yarrowia lipolytica strain capable of producing significant lipid amounts when cultivated on industrial fats. Biomass and cellular lipid evolution were successfully simulated, while the optimized parameter values were similar to those experimentally measured. The maximum specific formation rate of fat-free biomass seemed unaffected by the substrate fatty acid composition. On the contrary, the maximum concentration of lipid accumulated inside the yeast cell, as well as the maximum specific accumulation rate of cellular lipids, was favored in high stearic acid content media. The microorganism presented the tendency to degrade its accumulated lipids, although remarkable substrate fat amounts remained unconsummated in the culture medium. This degradation slowly occurred in the yeast cell as the specific rate of the intracellular carbon pool (storage lipid consumption) was significantly lower compared with that of the extracellular carbon pool (substrate fat). However, the fat-free biomass yield on storage lipids (g of fat-free biomass formed per g of storage lipids consumed) was higher than the one on the substrate (g of fat-free biomass formed per g of medium fat consumed). Received: 26 June 2002 / Accepted: 22 July 2002     

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.     

Stable adaptive algorithm for simultaneous estimation of time-varying parameters and state variables in aerobic bioprocesses

The application of modern model based control algorithms in the bioprocesses is hampered by the lack of accurate and cheap on-line sensors, capable of providing on-line measurements of the main process variables and parameters. In this paper, a new approach for estimation of immeasurable time-varying parameters and state variable is presented for a class of aerobic bioprocesses using only on-line measurements of the oxygen uptake rate. The approach consists in the design of a new parameter estimator of biomass growth rate and yield coefficient for oxygen consumption on the basis of the theory of adaptive estimation. The dynamical equation of the measurable reaction rate, oxygen uptake rate, is presented as a linear one with respect to the biomass growth rate and the yield coefficient for oxygen consumption. In this way, the structure of the proposed estimator becomes linear time-varying one. After some mathematical transformations, that structure is presented in a form, allowing to be derived the stability conditions using some theoretical results concerning the stability of adaptive observers. The estimates of the yield coefficient for oxygen consumption, the biomass concentration and specific growth rate are obtained then on the basis of the generated estimates using well known kinetic models of bioprocesses. With respect to previous similar approaches, the new estimation algorithm gives stable estimates not only of immeasurable state variable and reaction rates but likewise of an yield coefficient. The behavior of the proposed estimator is studied under inexact initial conditions, step changes of dilution rate and in the presence of measurement noise by simulations using a process model, which belongs to the investigated class of bioprocesses.     

Bayesian sequential inference for stochastic kinetic biochemical network models.

As postgenomic biology becomes more predictive, the ability to infer rate parameters of genetic and biochemical networks will become increasingly important. In this paper, we explore the Bayesian estimation of stochastic kinetic rate constants governing dynamic models of intracellular processes. The underlying model is replaced by a diffusion approximation where a noise term represents intrinsic stochastic behavior and the model is identified using discrete-time (and often incomplete) data that is subject to measurement error. Sequential MCMC methods are then used to sample the model parameters on-line in several data-poor contexts. The methodology is illustrated by applying it to the estimation of parameters in a simple prokaryotic auto-regulatory gene network.     

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     

On-line biomass measurements in bioreactor cultivations: comparison study of two on-line probes

Two on-line probes for biomass measurement in bioreactor cultivations were evaluated. One probe is based on near infrared (NIR) light absorption and the other on dielectric spectroscopy. The probes were used to monitor biomass production in cultivations of several different microorganisms. Differences in NIR probe response compared to off-line measurement methods revealed that the most significant factor affecting the response was cell shape. The NIR light absorption method is more developed and reliable for on-line in situ biomass estimation than dielectric spectroscopy. The NIR light absorption method is, however, of no significant use, when the cultivation medium is not clear, and especially in processes using adsorbents or solid matrix for the microorganism to grow on. The possibilities offered by dielectric spectroscopy are impressive, but the on-line probe technology needs to be improved.     

On-line measurements of culture fluorescence: Method and application

Summary In this paper a new probe allowing the measurement of NAD(P)H-dependent culture fluorescence in a bioreactor is presented. This sterilizable probe can be inserted in every bioreactor using a standard fitting of 25 mm. Under well defined conditions high specificity and sensitivity as well as high stability are further advantages of this probe. Application examples are given to demonstrate the operation possibilities of this fluorescence probe. In batch growth the culture fluorescence can be used for on-line estimation of biomass concentration. Metabolic alterations due to substrate of oxygen deficiency can easily be detected by fluorometric measurements. In kinetic studies the fluorescence probe is of great use because of a very small time delay.     

Model for on-line moisture-content control during solid-state fermentation

In this study we describe a model that estimates the extracellular (nonfungal) and overall water contents of wheat grains during solid-state fermentation (SSF) with Aspergillus oryzae, using on-line measurements of oxygen, carbon dioxide, and water vapor in the gas phase. The model uses elemental balances to predict substrate dry matter losses from carbon dioxide measurements, and metabolic water production, water used in starch hydrolysis, and water incorporated in new biomass from oxygen measurements. Water losses caused by evaporation were calculated from water vapor measurements. Model parameters were determined using an experimental membrane-based model system, which mimicked the growth of A. oryzae on the wheat grains and permitted direct measurement of the fungal biomass dry weight and wet weight. The measured water content of the biomass depended heavily on the moisture content of the solid substrate and was significantly lower than the estimated values reported in the literature. The model accurately predicted the measured overall water content of fermenting solid substrate during fermentations performed in a 1.5-L scraped drum reactor and in a 35-L horizontal paddle mixer, and is therefore considered validated. The model can be used to calculate the water addition required to control the extracellular water content in a mixed solid-state bioreactor for cultivation of A. oryzae on wheat.     

Nonlinear estimation of Monod growth kinetic parameters from a single substrate depletion curve.

Monod growth kinetic parameters were estimated by fitting sigmoidal substrate depletion data to the integrated Monod equation, using nonlinear least-squares analysis. When the initial substrate concentration was in the mixed-order region, nonlinear estimation of simulated data sets containing known measurement errors provided accurate estimates of the mu max, Ks, and Y values used to create these data. Nonlinear regression analysis of sigmoidal substrate depletion data was also evaluated for H2-limited batch growth of Desulfovibrio sp. strain G11. The integrated Monod equation can be more convenient for the estimation of growth kinetic parameters, particularly for gaseous substrates, but it must be recognized that the estimates of mu max, Ks, and Y obtained may be influenced by the growth rate history of the inoculum.     

Nonlinear estimation of Monod growth kinetic parameters from a single substrate depletion curve

Monod growth kinetic parameters were estimated by fitting sigmoidal substrate depletion data to the integrated Monod equation, using nonlinear least-squares analysis. When the initial substrate concentration was in the mixed-order region, nonlinear estimation of simulated data sets containing known measurement errors provided accurate estimates of the mu max, Ks, and Y values used to create these data. Nonlinear regression analysis of sigmoidal substrate depletion data was also evaluated for H2-limited batch growth of Desulfovibrio sp. strain G11. The integrated Monod equation can be more convenient for the estimation of growth kinetic parameters, particularly for gaseous substrates, but it must be recognized that the estimates of mu max, Ks, and Y obtained may be influenced by the growth rate history of the inoculum.     

Respirometric assay for biofilm kinetics estimation: parameter identifiability and retrievability

Currently, no fast and accurate methods exist for measuring extant biokinetic parameters for biofilm systems. This article presents a new approach to measure extant biokinetic parameters of biofilms and examines the numerical feasibility of such a method. A completely mixed attached growth bioreactor is subjected to a pulse of substrate, and oxygen consumption is monitored by on-line measurement of dissolved oxygen concentration in the bulk liquid. The oxygen concentration profile is then fit with a mechanistic mathematical model for the biofilm to estimate biokinetic parameters. In this study a transient biofilm model is developed and solved to generate dissolved oxygen profiles in the bulk liquid. Sensitivity analysis of the model reveals that the dissolved oxygen profiles are sufficiently sensitive to the biokinetic parameters-the maximum specific growth rate coefficient (insertion markμ) and the half-saturation coefficient (Ks)-to support parameter estimation if accurate estimates of other model parameters can be obtained. Monte Carlo simulations are conducted with the model to add typical measurement error to the generated dissolved oxygen profiles. Even with measurement error in the dissolved oxygen profile, a pair of biokinetic parameters is always retrievable. The geometric mean of the parameter estimates from the Monte Carlo simulations prove to be an accurate estimator for the true biokinetic values. Higher precision is obtained for insertion markμ estimates than for Ks estimates. In summary, this theoretical analysis reveals that an on-line respirometric assay holds promise for measuring extant biofilm kinetic parameters. Copyright 1998 John Wiley & Sons, Inc.     

Effect of different nitrogen sources on the biosynthesis of lipase by Oospora lactis

The effect of inorganic and organic nitrogen compounds on the synthesis of biomass and extracellular lipase by Oospora lactis was studied. Among the inorganic nitrogen sources ammonium sulphate and ammonium secondary phosphate and among the organic nitrogen sources yeast autolysate proved to be most beneficial for the lipase synthesis. Lipase activity and biomass accumulation in the medium containing yeast autolysate were greater than in the media containing the above ammonium salts. Lipase synthesis reached maximum in the nutrient medium containing yeast autolysate (0.7%) and ammonium sulphate (0.3%).     

Parametric sensitivity analysis and reduction of a detailed nutritional model of plant cell cultures

A kinetic model of plant nutrition described by Cloutier et al. (Cloutier et al., 2008. Biotechnol Bioeng 99:189-200) is progressively simplified so as to obtain a predictive model that describes the evolution of the biomass and the extracellular and intracellular concentrations of three determining nutrients, that is, free intracellular nitrogen, phosphate, and carbohydrate compounds. Three techniques of global sensitivity analysis are successively applied to assess the model parameter influence and potential correlation. The resulting dynamic model is able to predict plant growth for the two most encountered plant bioprocesses, namely suspension cells and hairy roots.     

Development of a phenomenological modeling approach for prediction of growth and xanthan gum production using Xanthomonas campestris

An unstructured kinetic model for xanthan production is described and fitted to experimental data obtained in a stirred batch reactor. The culture medium was composed of several nitrogen sources (soybean hydrolysates, ammonium and nitrate salts) consumed sequentially. The model proposed is able to describe this sequential consumption of nitrogen sources, the consumption of inorganic phosphate and carbon, the evolution of biomass, and production of xanthan. The parameter estimation has been performed by fitting the kinetic model in differential form to experimental data. Runs of the model for simulating xanthan gum production as a function of the initial concentration of inorganic phosphate have shown the positive effect of phosphate limitation on xanthan yield, though diminishing rates of production. The model was used to predict the kinetic parameters for a medium containing a 2-fold lower initial phosphate concentration. When tested experimentally, the measured fermentation parameters were in close agreement with the predicted model values, demonstrating the validity of the model.     

Adaptive on-line simulation of bioreactors: Fermentation monitoring and modeling system

Summary In order to study and control fermentation processes, indirect on-line measurements and mathematical models can be used. Here an on-line model for fermentation processes is presented. The model is based on atom and partial mass balances as well as on stability equations for the protolytes. The model is given an adaptive form by including transport equations for mass transfer and expressions for the fermentation kinetics. The state of the process can be estimated on-line using the balance component of the model completed with measurement equations for the input and the output flows of the process. Adaptivity is realized by means of on-line estimation of the parameters in the transport and kinetic expressions using recursive regression analysis. On-line estimation of the kinetic and mass transfer parameters makes model-based predictions possible and enables intelligent process control while facilitating testing of the validity of the measurement variables. A practical MS-Windows 3.1 model implementation called FMMS—Fermentation Monitoring and Modeling System is shown. The system makes it easy to configure the operating conditions for a run. It uses Windows dialogs for all set-ups, model configuration parameters, elemental compositions, on-line measurement devices and signal conditioning. Advanced on-line data analysis makes it possible to plot variables against each other for easy comparison. FMMS keeps track of over 100 variables per run. These variables are either measured or estimated by the model. Assay results can also be entered and plotted during fermentation. Thus the model can be verified almost instantly. Historical fermentation runs can be re-analyzed in simulation mode. This makes it possible to examine different signal conditining filters as well as the sensitivity of the model. Combined, the data analysis and the simulation mode make it easy to test and develop model theories and new ideas.