An enzyme kinetic model for describing fermentation processes

An enzyme kinetic model has been proposed to describe fermentation processes. This type of model was chosen because it is biologically sound, can incorporate all of the important engineering control variables, and can draw upon, in its development, the extensive kinetic literature. An intial qualitative test for this model was made on the gluconic acid fermentation. A necessary check of the model was that Monod's empirical cell growth and yield equations were derived as a special case. The model also offered an explanation for the hysteresis behavior of the gluconic acid production rate as a function of gluconolactone.     

Nonlinear observation of specific growth rate in aerobic fermentation processes

Simple nonlinear observers for the on-line estimation of the specific growth rate from presently attainable real-time measurements are presented. The proposed observers do not assume or require any model for the specific growth rate and they are very successful in accurately estimating this parameter. Moreover, they are very easy to implement and to calibrate. Indeed, due to the particular structure of their gain, their tuning is reduced to the calibration of a single parameter. Simulation results obtained under different operating conditions are given in order to highlight the performances of the proposed estimators.     

Nonlinear estimation of specific growth rate for aerobic fermentation processes

The specific growth rate of the biomass, a very important parameter of almost every fermentation process, cannot be measured directly or estimated from related variables, as the concentrations of biomass, substrates, or products, due to the lack of reliable and cheap sensors. In this article a stable adaptive estimator of the specific growth rate is designed for those aerobic processes where the measurement of the oxygen uptake rate is available on-line. This particular approach can be applied also for other reaction rates if the model of the process satisfies some very general assumptions, which make the dynamics of the measured reaction rate a nonlinear function only of two unknown parameters, the specific growth rate and its time derivative. With respect to a previous similar approach, the new estimator has one additional parameter and a different nonlinear structure. From the analysis of the dynamics of the estimation error, a tuning criterion is derived, by which the two different algorithms can be compared under similar conditions. Simulation results show a good performance of both estimators for various kind of processes and disturbances. (c) 1995 John Wiley & Sons, Inc.     

A comprehensive model of simultaneous denitrification and methanogenic fermentation processes

The denitrification process was incorporated into the IWA Anaerobic Digestion Model No. 1 (ADM1) in order to account for the effect of denitrification on the methanogenic fermentation process. The model was calibrated and optimized using previously published experimental data and kinetic parameter values obtained with a mixed, mesophilic (35°C) methanogenic culture. Model simulations were used to predict the effect of nitrate reduction on the methanogenic fermentation process in batch, semi‐continuous, and continuous flow reactors experiencing operational changes and/or system disturbances. The extended model clearly revealed the importance of substrate competition between denitrifiers and non‐denitrifiers as well as the impact of N‐oxide inhibition on process interactions between fermentation, methanogenesis, and denitrification. Biotechnol. Bioeng. 2010;105: 98–108. © 2009 Wiley Periodicals, Inc.     

The role of model selection in describing stochastic ecological processes

A great deal of variation in ecological processes can be generated through variation in environmental conditions. Models describing the underlying processes should be able to account for this variation. However, models may not be flexible enough, so that different realizations of a process may be better described by different models. This may lead to uncertainty in model selection.
Here we examine the question of whether two empirical models can provide consistent fits to different realizations of a process affected by environmental variation. We further examine the sensitivity of the model predictions to the amount of data available and the selection of the model. To study this, we simulated pollen dispersal patterns under varying wind conditions and then investigated whether the datasets consistently supported the same model. The role of the model selection and the impact of the spatial range over which the dispersal distances were observed were assessed by comparing model predictions at long dispersal distances.
There was no consistent pattern of one model providing a better fit than the other across simulations. The model providing better fit varied depending on the range of distances over which the dispersal patterns were observed, and on the amount of long-distance dispersal. The model predictions were found to be very sensitive to the selection of the model.
The variation between datasets produced with the same underlying mechanisms cannot be easily described using one model, which also limits our ability to reliably predict the underlying process. Therefore, the amount of information about a model choice provided by an individual field study may be rather limited. If we are to understand processes that are affected by environmental variation then we have to observe the range of possible outcomes of the processes under varying spatio-temporal conditions.     

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.     

Relating damped oscillations to sustained limit cycles describing real and ideal batch fermentation processes

A batch fermentation model is presented in which the specific growth rate and yield functions are chosen such that sustained oscillations in both the cell and substrate concentration occur. This phenomenon is shown to be a Hopf bifurcation in the underlying system of non-linear ordinary differential equations which comprises the model. It is shown that for oscillations in the substrate concentration to occur it is necessary for the yield term to depend on both the cell and substrate levels.     

A model describing nonlinearities in hearing by active processes with saturation at 40 dB

Data from literature related to nonlinearities of the peripheral part of the hearing system are collected and extended by results from measurements of acoustical responses, masking, cubic difference tones and Zwicker tones. The data indicate 40 dB as a significant value for the dynamic range in neurophysiology as well as for the sensation level in psychoacoustics dividing the total level range into two areas of different characteristics. A preliminary model assuming that the outer hair cells act as an amplifier which contains saturation (corresponding to 40 dB) and feed back to sensitize the inner hair cells is used to describe the measured effects at least qualitatively.     

Glucose overflow metabolism and mixed-acid fermentation in aerobic large-scale fed-batch processes with Escherichia coli

Industrial 20-m³-scale and laboratory-scale aerobic fed-batch processes with Escherichia coli were compared. In the large-scale process the observed overall biomass yield was reduced by 12% at a cell density of 33 g/l and formate accumulated to 50 mg/l during the later constant-feeding stage of the process. Though the dissolved oxygen signal did not show any oxygen limitation, it is proposed that the lowered yield and the formate accumulation are caused by mixed-acid fermentation in local zones where a high glucose concentration induced oxygen limitation. The hypothesis was further investigated in a scale-down reactor with a controlled oxygen-limitation compartment. In this scale-down reactor similar results were obtained: i.e. an observed yield lowered by 12% and formate accumulation to 238 mg/l. The dynamics of glucose uptake and mixed-acid product formation (acetate, formate, d-lactate, succinate and ethanol) were investigated within the 54 s of passage time through the oxygen-limited compartment. Of these, all except succinate and ethanol were formed; however, the products were re-assimilated in the oxygen-sufficient reactor compartment. Formate was less readily assimilated, which accounts for its accumulation. The total volume of the induced-oxygen-limited zones was estimated to be 10% of the whole liquid volume in the large bioreactor. It is also suggested that repeated excretion and re-assimilation of mixed-acid products contribute to the reduced yield during scale-up and that formate analysis is useful for detecting local oxygen deficiency in large-scale E. coli processes. Received: 7 November 1998 / Received revision: 4 February 1999 / Accepted: 5 February 1999     

A metabolic model of cellular energetics and carbon flux during aerobic Escherichia coli fermentation

An integrated metabolic model for the production of acetate by Escherichia coli growing on glucose under aerobic conditions was presented previously (Ko et al., 1993). The resulting model equations can be used to explain phenomena often observed with industrial fermentations, i.e., increased acetate production which follows from high glucose uptake rate, a low dissolved oxygen concentration, a high specific growth rate, or a combination of these conditions. However, several questions still need to be addressed. First, cell composition is growth rate and media dependent. Second, the macromolecular composition varied between E. coli strains. And finally, a model that represents the carbon fluxes between the Embden-Meyerhof-Parnas (EMP) and the hexose monophosphate (HMP) pathways when cells are subject to internal and/or external stresses is still not well defined. In the present work, we have made an effort to account for these effects, and the resulting model equations show good agreement for wild-type and recombinant E. coli experimental data for the acetate concentration, the onset of acetate secretion, and cell yield based on glucose. These results are useful for optimizing aerobic E. coli fermentation processes. More specifically, we have determined the EMP pathway carbon flux profiles required by the integrated metabolic model for an accurate fit of the acetic acid profile data from a wild-type E. coli strain ML308. These EMP carbon flux profiles were correlated with a dimensionless measurement of biomass and then used to predict the acetic acid profiles for E. coli strain F-122 expressing human immunodeficiency virus-(HIV(528)) beta-galactosidase fusion protein. The effect of different macromolecular compositions and growth rates between these two E. coli strains required a constant scaling factor for improved quantitative predictions.     

A macroscopic model of traffic jams in axons

The purpose of this paper is to develop a minimal macroscopic model capable of explaining the formation of traffic jams in fast axonal transport. The model accounts for the decrease of the number density of positively (and negatively) oriented microtubules near the location of the traffic jam due to formation of microtubule swirls; the model also accounts for the reduction of the effective velocity of organelle transport in the traffic jam region due to organelles falling off microtubule tracks more often in the swirl region. The model is based on molecular-motor-assisted transport equations and the hydrodynamic model of traffic jams in highway traffic. Parametric analyses of the model’s predictions for various values of viscosity of the traffic flow, variance of the velocity distribution, diffusivity of microtubule-bound and free organelles, rate constants for binding to and detachment from microtubules, relaxation time, and average motor velocities of the retrograde and anterograde transport, are carried out.     

A database system for fermentation processes

Data base management is needed in the whole industries, particularly in the fermentation industry, whose jobs are tedious yet require carefulness. The most important problem in the database system is not how to collect many informations, but how to handle the meaningful ones.The authors have recently developed an on-line monitoring and control system for the fermentation processes in co-operation with Fuji Facom Co. Ltd. and Komatsugawa Chemical Engineering Co. Ltd.This system enables us to measure directly those concentrations in fermentation systems which have been measured by offline so far, such as cell mass, substrate and metabolic products. The physiological activities of a microorganism, such as specific rate of cellular growth, that of substrate consumption, that of metabolites production, etc., became estimable precisely by eliminating the effect of noises.By enlarging the function of our monitoring and control system, we have developed a database system which is applicable in job scheduling not only in the laboratory but also in the production line, in automatic resource allocation and fault analyses of the fermentation processes.     

Validation of a model describing two-dimensional heat transfer during solid-state fermentation in packed bed bioreactors

A two-dimensional heat transfer model was validated against two experimental studies from the literature which describe the growth of Aspergillus niger during solid-state fermentation in packed bed bioreactors. With the same set of model parameters, the two-dimensional model was able to describe both radial temperature gradients, which dominated in one of the studies, and axial temperature gradients, which dominated in the other study. The sensitivity of the model predictions to the characteristics of the substrate and the microbe were explored. The temperatures reached in the column are most sensitive to parameters which affect the peak heat load, including the substrate packing density, the maximum specific growth rate, and the maximum biomass concentration. Even though the bed is assumed to be aerated with saturated air, the increase in temperature with bed height increases the water-carrying capacity of the air and therefore enables evaporation to contribute significantly to cooling. The model suggests that evaporation can remove as much as 78% of the heat from the bed during times of peak heat generation. Our model provides a tool which can guide the design and operation of packed bed bioreactors. However, further improvements are necessary to do this effectively, the most important of which is the incorporation of a water balance.     

Extremum seeking scheme for continuous fermentation processes described by an unstructured fermentation model

This paper examines the problem of maximising the productivity of a class of fermentation processes described by an unstructured fermentation process model. For a given dilution rate, an extremum seeking adaptive control has been used to maximise the productivity of a fermentation process. The concept behinds the extremum seeking method is to iteratively adjust the feed substrate rate in order to steer the process to yield a maximum productivity. The main advantage of the extremum seeking adaptive control is it does not require any structural information of the modeling uncertainty.     

Recycle in fermentation processes

Until recently, the recycle of the solid (microbial), liquid, or gaseous phases in microbiological processes has only been practiced rarely, with the notable exception of activated sludge processes for wastewater treatment, where recycling of a large fraction of the microbial phase is essential for process stability and performance. During the last decade, the economic impact of a number of politically motivated changes with respect to energy and feedstock costs and availability, and legislation directed towards markedly higher levels of environmental protection have encouraged the evaluation and subsequent development of recycle technology in the fermentation industry. Many of the developments have occurred in isolation and some have failed to result in either an improvement in process economics or any reduction in the quantity of pollutants discharged. This article seeks to review the present diversity of approaches to recycle technology in fermentation processes in order to provide a sensible basis for future developments.     

A reassessment of mixing cost in fermentation processes

The gas–liquid oxygen transfer rate is a key step in the production of antibiotics in submerged fermentation. If the gas–liquid oxygen mass transfer rate is not equal to the required liquid–solid oxygen mass transfer rate at a particular cell concentration, then productivity of the particular fermentation operation will not be the maximum possible value. One way to increase the productivity of a given fermentation tank installation is to increase the cell concentration and to increase the oxygen transfer by changing the mixer and air supply to match the new requirements. In order to evaluate the cost of making this change to the larger mixing equipment, a typical cost example is given which can easily be modified for other combinations of production cost and mixer cost. As an example, it is seen that a considerable savings can result from a given installation by primarily changing the oxygen transfer ability of the equipment to utilize a given fermentor more efficiently. Production cost savings of 8 to 25% are shown in the example cited.     

A multiphase model describing vascular tumour growth

In this paper we present a new model framework for studying vascular tumour growth, in which the blood vessel density is explicitly considered. Our continuum model comprises conservation of mass and momentum equations for the volume fractions of tumour cells, extracellular material and blood vessels. We include the physical mechanisms that we believe to be dominant, namely birth and death of tumour cells, supply and removal of extracellular fluid via the blood and lymph drainage vessels, angiogenesis and blood vessel occlusion. We suppose that the tumour cells move in order to relieve the increase in mechanical stress caused by their proliferation. We show how to reduce the model to a system of coupled partial differential equations for the volume fraction of tumour cells and blood vessels and the phase averaged velocity of the mixture. We consider possible parameter regimes of the resulting model. We solve the equations numerically in these cases, and discuss the resulting behaviour. The model is able to reproduce tumour structure that is found in vivo in certain cases. Our framework can be easily modified to incorporate the effect of other phases, or to include the effect of drugs.