A hybrid asymptotic-Kalman observer for bioprocesses

The exponential observers (extended Kalman or Luenberger observers, high gain observers) allow the use of a tuning parameter for managing the rate of convergence of the state estimate towards the true state. But their results are strongly dependent on the model quality (especially the kinetic model in bioprocesses). On the other hand, asymptotic observers (like the observer of Bastin and Dochain) have a rate of convergence which is a function of the experimental conditions (namely the dilution rate). However, this lack of tuning parameter is compensated by the absence of need for any kinetic model. In this paper, a hybrid technique is proposed which allows to jointly estimate the state and identify on-line the confidence on the kinetic model. The two limit cases (100 and 0 confidence) allow to recover rigorously the extended Kalman filter and the asymptotic observer of Bastin and Dochain. A simulation example (a fed-batch bacterial culture) is proposed and exhibits very satisfactory results.     

Reaction rate reconstruction from biomass concentration measurement in bioreactors using modified second-order sliding mode algorithms

This paper deals with the estimation of unknown signals in bioreactors using sliding observers. Particular attention is drawn to estimate the specific growth rate of microorganisms from measurement of biomass concentration. In a recent article, notions of high-order sliding modes have been used to derive a growth rate observer for batch processes. In this paper we generalize and refine these preliminary results. We develop a new observer with a different error structure to cope with other types of processes. Furthermore, we show that these observers are equivalent, under coordinate transformations and time scaling, to the classical super-twisting differentiator algorithm, thus inheriting all its distinctive features. The new observers' family achieves convergence to time-varying unknown signals in finite time, and presents the best attainable estimation error order in the presence of noise. In addition, the observers are robust to modeling and parameter uncertainties since they are based on minimal assumptions on bioprocess dynamics. In addition, they have interesting applications in fault detection and monitoring. The observers performance in batch, fed-batch and continuous bioreactors is assessed by experimental data obtained from the fermentation of Saccharomyces Cerevisiae on glucose.     

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.     

On-line estimation of biodegradation in an unsaturated soil

The objective of this study was to develop a model-based estimator of biodegradation in unsaturated soil. This would allow real-time assessment of the efficiency of treatment bioprocesses, such as bioventilation and biopile, and eventually permit optimization through the implementation of control strategies. Based on a reduced-order model, an asymptotic observer was designed to estimate on-line the contaminant concentration, using carbon dioxide measurement. Two observer-based estimators were built to approximate: (1) the specific microbial growth rate; and (2) the biocontact kinetics representing the soil resistance to contaminant biodegradation. State observers and parameter estimators were confronted with the experimental results of biodegradation in microcosms. Hexadecane was used as the model compound, representing petroleum hydrocarbons. Three water contents, corresponding to 20%, 50% and 80% of the water-holding capacity, were tested. The asymptotic observer is able to predict hexadecane depletion with an error on the overall time trajectories of 13%, 8% and 4% for the dry, intermediate and wet soils, respectively, which is acceptable given that all the biokinetic parameters were identified from a biodegradation experiment in liquid phase. The observer-based estimator of the specific microbial growth rate, based on the CO₂ measurement, was successfully calibrated using the off-line measurements of hexadecane as validation data, and allowed estimation of the time when biodegradation switched from a microbial to a biocontact limitation. The biocontact kinetics was also identified on-line, using an estimator based on the hexadecane not in biocontact. These results are very encouraging with respect to the potential for on-line assessment of the performance of treatment bioprocesses in unsaturated soils.     

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.     

Geomicrobial Kinetics: Extrapolating Laboratory Studies to Natural Environments

Predicting metabolic rates and population sizes of microorganisms in natural environments is a central problem in geomicrobiology. Such predictions can be made on the basis of a thermodynamically consistent rate law that accounts for both kinetic and thermodynamic controls on microbial metabolism. Application of the rate law requires kinetic and growth parameters, the values of which have been determined for pure and mixed cultures growing in laboratory reactors. However, not all parameter values derived from laboratory studies can be validly applied to the environment. This article illustrates a best-choice approach for extrapolating experimentally-derived parameter values to natural environments, using microbial sulfate reduction coupled to acetate oxidation as an example. We compiled kinetic and growth parameters determined by previous laboratory studies and evaluated their applicability to natural environments. Our results suggest that some parameters, such as rate constants and maximum growth yields, can be applied directly to the environment; others, such as half-saturation constants and specific maintenance rates, are best determined using samples recovered from the environment of interest. The best-choice parameter values were applied to simulation of acetotrophic sulfate reduction in the sediments of a freshwater lake. Our analysis shows that the best-choice approach reduces the tasks of parameter fitting and simplifies the modeling exercise. The proposed approach also ensures that parameters in use are consistent with the physiology of indigenous microorganisms, and relevant to the environment of interest.     

Little tern breeding success in artificial and natural habitats: modelling population growth under uncertain vital rates

As a consequence of habitat loss, breeding in man-made habitats has become increasingly common for many coastal breeding bird species. While artificial sites provide valuable substitutes, they may also be more attractive, and importantly, differ in quality from natural sites. Therefore, information on habitat specific breeding success and their potential for supporting stable populations are needed. We compared little tern (Sternula albifrons) breeding success (nest and hatching success) between natural habitat (sandy beaches) and artificial port habitat at Bothnian Bay, Finland from 2006 to 2011. We further reviewed published estimates on pre-fledging and adult survival for little terns and least terns (Sternula antillarum), and used these ranges to estimate plausible parameter spaces for population growth rates given our estimates of breeding success. Nest success was among the highest reported for little terns in the artificial habitat (82 %) while being lower in the natural habitat (58 %). This difference may have resulted from differences in colony sizes and levels of disturbance. Hatching success did not differ significantly, but the percentage of successful nests containing unhatched eggs was twice as high in the natural habitat. The parameter spaces for population growth rates indicated that the artificial habitat has good potential to sustain stable populations (66 % positive growth rate) while for the natural habitat this potential was lower (37 % positive growth rate). While our results suggest that artificial habitats can be very productive breeding sites for habitat deprived tern populations, management should concentrate on improving both habitats with emphasis on natural sites.     

Rheological changes of Aspergillus awamori broth during amyloglucosidase production

Two kinds of mathematical correlations are proposed, one between the biomass concentration and the rheological parameter consistency index (K) from the 'Power law' and another between either the specific growth rate or the specific glucoamylase production rate and K. Experimental data from Aspergillus awamori batch cultivations, with initial polysaccharide concentrations in the range of 20 to 180 g.L, were used to define these correlations.     

Modelling Visual Change Detection and Identification under Free Viewing Conditions

We examined whether the abilities of observers to perform an analogue of a real-world monitoring task involving detection and identification of changes to items in a visual display could be explained better by models based on signal detection theory (SDT) or high threshold theory (HTT). Our study differed from most previous studies in that observers were allowed to inspect the initial display for 3s, simulating the long inspection times typical of natural viewing, and their eye movements were not constrained. For the majority of observers, combined change detection and identification performance was best modelled by a SDT-based process that assumed that memory resources were distributed across all eight items in our displays. Some observers required a parameter to allow for sometimes making random guesses at the identities of changes they had missed. However, the performance of a small proportion of observers was best explained by a HTT-based model that allowed for lapses of attention.     

Daughter cells as an important factor in determining the physiological state of yeast populations

Cells of Candida utilis grown in a single-stage chemostat at D = 0.05, 0.1, 0.25, and 0.35 hr^?l were separated into a fraction of scar-bearing mother cells and a fraction of scar-free daughter cells. The scar-free cells were transferred into small batch cultures where the length of the maturation phase, changes in length and width of cells, specific growth rate, and specific rate of RNA and protein synthesis were examined for 5 hr. The daughter cells grown at D = 0.05 hr^?1 were very small at the moment of separation from the mother cells (about one-third of the mother cell). Their maturation phase (in a batch culture), at the beginning of which they attain the specific growth rate approaching the μ_max of the strain used, lasts for 3 hr. On the other hand, daughter cells grown at D = 0.35 hr^?1 are almost the same size as the mother cells at the moment of separation. After transfer to a batch culture they begin to bud almost immediately. Similarly, in their other morphological and physiological parameters they differ strikingly from immature daughter cells which are formed at low specific growth rates. The importance of these differences from the point of view of mathematical modeling of growth processes is discussed.     

The constant gene orf14.9, which belongs to the variable eps (exopolysaccharide) cluster, is involved in the cell growth of Streptococcus thermophilus

In Streptococcus thermophilus, the eps clusters involved in exopolysaccharide (EPS) biosynthesis are very polymorphic, nevertheless they all contain a highly conserved sequence corresponding to that of orf14.9. This open reading frame (ORF) is transcribed in a reverse direction with respect to eps genes. Amino acid sequence analysis showed a possible transmembrane location of the putative Orf14.9 protein but did not permit a proposed function. Insertional mutants of orf14.9 were obtained in strains NST2280 and A054 of S. thermophilus. EPS yields of these mutants are similar to those of their respective wild strains, suggesting that orf14.9 does not modify the quantity of produced EPS. Growth parameter determination for wild strains and their respective mutants showed that orf14.9 is involved in the cell growth of S. thermophilus.     

Parameter identification of a model of yeast cultivation process with neural network

A mathematical model of yeast cultivation process has been proposed in [1]. The present paper describes procedure for parameter identification of this model. The obtained numerical values of the parameters of the model allow to estimate the specific growth rate μ.     

An algorithmic approach to constructing the on-line estimation system for the specific growth rate

The objective of this article is to propose an algorithm for the on-line estimation of the specific growth rate in a batch or a fed-batch fermentation process. The algorithm shows the practical procedure for the estimation method utilizing the macroscopic balance and the extended Kalman filter. A number of studies of the on line estimation have been presented. However, there are few studies discussing about the selection of the observed variables and for the tuning of some parameters of the extended Kalman filter, such as covariance matrix and initial values of the state.The beginning of this article is devoted to explain the selection of the observed variable. This information is very important in terms of the practical know-how for using technique. It is discovered that the condition number is a practically useful and valid criterion for number is a practically useful and valid criterion for choosing the variable to be observed.Next, when the extended Kalman filter in applied to the online estimation of the specific growth rate, which is directly unmeasurable, criteria for judging the validity of the estimated value from the observed data are proposed. Based on the proposed criterial, the system equation of the specific growth rate is selected and initial value of the state variable and covariance matrix of the system noises are adjusted. From many experiments, it is certified that the specific growth rate in the batch or fed -batch fermentation can be estimated accurately by means of the algorithm proposed here. In these experiments, that is, when the cell concentration is measured directly, the extended Kalman filter using the convariance matrix with a constant element can estimate more accurately values of the specific growth rate than the adaptive extended Kalman filter does.     

Regulation of nitrogen metabolism in Escherichia coli and Klebsiella aerogenes: studies with the continuous-culture technique.

Ammonia-nitrogen-limited continuous cultures of Escherichia coli and Klebsiella aerogenes contain induced levels of glutamine synthetase that is deadenylyated (i.e., fully active). In the presence of excess ammonia or glutamate in glucose-limited cultures of E. coli, glutamine synthetase is repressed and adenylylated (inactive). The average state of adenylylation (n) is a linear function of the specific growth rate. At low specific growth rates, glutamine synthetase is adenylylated; as the specific growth rate increases, n decreases, approaching 0 to 2 at rapid growth rates. The average state of adenylylation correlates well with the intracellular concentrations and ratios of alpha-ketoglutarate and glutamine, which are key effectors in the adenylylation-deadenylylation systems. E. coli and K. aerogenes differ markedly in their growth yields, growth rates, and enzymatic composition during nitrogen limitation. The data suggest that, unlike K. aerogenes, E. coli W uses glutamate dehydrogenase to incorporate ammonia during nitrogen limitation. In E. coli, glutamate dehydrogenase is progressively induced during nitrogen limitation when mu (growth rate) approaches mumax. In contrast, in K. aerogenes glutamate dehydrogenase is repressed during nitrogen limitation, whereas glutamate synthase, an alternative supplier of glutamate to the cell, is induced. Data are presented that support the regulatory schemes proposed for the control of glutamine synthetase activity by induction-repression phenomena and adenylylation-deadenylylation reaction. We propose that the intracellular ratio of alpha-ketoglutarate to glutamine may be the most important physiological parameter in determining the activity of glutamine synthetase.     

Messenger RNA potential and the delay before exponential decay of messages

Potential is a parameter of messenger RNA decay that measures the ability of a message population to continue to initiate complete translations. It can be measured from the start of induction using a specific inhibitor of translation-initiation. With very short inductions it can be seen that the potential of the β-galactosidase message is not lost at a constant exponential rate until a time (delay time) approximately equal to the time required to synthesize the β-galactosidase message. The capacity to make enzyme declines only after the induction lag and its subsequent decay shows a somewhat longer delay; unlike potential, capacity is also affected by the variable rate of ribosome movement. The delays in loss of potential and capacity are consistent with either of two mechanisms: (1) the message must be completed before attack at its starting end, or (2) two or more separate events (or hits) with specific time constants are needed to inactivate. Even at very low growth temperatures, functional decay kinetics are consistent with either mechanism, as is the mass decay of β-galactosidase message at 37 °C. Messages for anthranilate synthetase and galactoside acetyl-transferase do not require two hits to inactivate, but the data cannot determine if there is a delay equal to their synthesis time. Either β-galactosidase message is exceptional and, as opposed to other messages, requires two or more hits to be inactivated, or Escherichia coli messages generally do not commence to decay until they are completed.     

Tissue growth and cancer

Food and metabolic waste products, insofar as they act upon the hereditary substrate of cells, are the most important factors governing tissue growth. Equations describing the growth of tissues are derived in consideration of this fact. A quantity is found in these equations which, if slightly changed, results in very great changes in the growth rate of the tissue, where such very great changes are interpretable as neoplastic growth. The relationship between our equations and similar equations which others have proposed is discussed.     

Succinate dehydrogenase activity of Escherichia coli cells after heat stress and during the reparative process

The resting cells of different E. coli cells remained viable after their heating at 48 degrees C for 30 min. The activity of their succinate dehydrogenase (SDH) (EC 1.3.99.1) was not more than 50% of the control one. When the cells were inoculated after a heat stress into a peptone medium, they started to grow at a high rate. However, their maximal specific growth rate mu and the overall biomass yield were less than in the control. The SDH activity of the cells reached the original level by the end of the logarithmic growth phase. This did not happen when the cells were incubated in 0.14 M NaCl for a time necessary for the culture to reach the end of the logarithmic growth phase. The SDH activity (in absolute values) of cell-free extracts was not greater than 35% of the cell SDH activity. The SDH activity of the cell-free extracts did not change after their heating at 48 degrees C. The SDH activity of E. coli cells is recommended to be used as a parameter indicative of their stress state.     

Transient kinetics of hybridoma growth and monoclonal antibody production in serum-limited cultures

A quantitative study of the influence of initial serum concentration on hybridoma growth rate, maximum viable and total cell yield, and specific antibody production rate is presented. The specific growth rate varied in a Monod fashion with initial serum levels (2-10% FCS), giving K(m) = 1.6 v/v% and mu(max) = 0.92 d(-1). The maximum cell yields (total and viable) were linear with initial serum level, indicating stoichiometric as well as kinetic limitation by serum component(s). The specific antibody production rate for each individual run fitted well to a non-growth-associated model. However, the non-growth-associated parameter varied monotonically with initial serum concentration, suggesting the catalytic role of serum component(s) in antibody production. Also, glutamine was utilized inefficiently, with at least a third of it secreted back into the culture supernate in the form of glutamate. While very simple model equations describe the specific growth and product formation rate for an individual batch run, the larger picture indicates need for a more detailed unstructured or structured model.     

Estimation of true growth and product yields in aerobic cultures

In the microbial production of useful products, it is important to understand the allocation of substrate energy for maintanance, growth, and product formation. Methods are presented to obtain point and 95% confidence interval estimates for the true growth yield parameter, true product yield parameter, and the maintenance parameter. Methods are presented which allow all data to be used simultaneously for those cases where more than the minimum number of measurements are made at each specific growth rate (or dilution rate). Three estimation methods and two forms of the energy allocation equations are investigated. Point estimates are similar for the three methods, but interval estimates are considerably larger for one of the three methods. The results depend on the form of the equations.     

Model simulation and analysis of perfusion culture of mammalian cells at high cell density.

Rate equations recently proposed by the authors for growth, death, consumption of nutrients, and formation of lactic acid, ammonium, and monoclonal antibody of hybridoma cells are used to simulate and analyze the behavior of perfusion cultures. Model simulations are in good agreement with experimental results from three different cell lines under varied perfusion and cell bleed rates except for cultures with very low viability. Analysis of simulations and experimental results indicates that in perfusion cultures with a complete cell separation cell bleed rate is a key parameter that strongly affects all the process variables, whereas the perfusion rate mainly affects the total and viable cell concentrations and the volumetric productivity of monoclonal antibody. Growth rate, viability, and specific perfusion rate of cells are only a function of the cell bleed rate. This also applies to cultures with partial cell separation in the permeate if the effective cell bleed rate is considered. It is suggested that the (effective) cell bleed rate of a perfusion culture should be carefully chosen and controlled separately from the perfusion rate. In general, a low cell bleed rate that warrants a reasonable cell viability appears to be desirable for the production of antibodies. Furthermore, model simulations indicate the existence of an optimum initial glucose concentration in the feed. For the cell lines considered, the initial glucose concentration used in normal cell culture media is obviously too high. The initial glutamine concentration can also be reduced to a certain extent without significantly impairing the growth and antibody production but considerably reducing the ammonia concentration. The mathematical model can be used to predict these optimum conditions and may also be used for process design.