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.     

Effect of resting smooth muscle length on contractile response in resistance airways

We studied the effect of resting smooth muscle length on the contractile response of the major resistance airways (generations 0-5) in 18 mongrel dogs in vivo using tantalum bronchography. Dose-response curves to 10(-10) to 10(-7) mol/kg methacholine (MCh) were generated [at functional residual capacity (FRC)] by repeated intravenous bolus administration using tantalum bronchography after each dose. Airway constriction varied substantially with dose-equivalent stimulation and varied sequentially from trachea (8.8 +/- 2.2% change in airway diam) to fifth-generation bronchus (49.8 +/- 3.0%; P less than 0.001). Length-tension curves were generated for each airway to determine the airway diameter (i.e., resting in situ smooth muscle length) at which maximal constriction was elicited using bolus intravenous injection of 10(-8) mol/kg MCh. A Frank-Starling relationship was obtained for each airway; the transpulmonary pressure at which maximal constriction was elicited increased progressively from 2.50 +/- 1.12 cmH2O for trachea (approximately FRC) to 18.3 +/- 1.05 cmH2O for fifth-generation airways (approximately 50% TLC) (P less than 0.001). A similar relationship was obtained when change in airway diameter was plotted as a function of airway radius. We demonstrate substantial heterogeneity in the lung volumes at which maximal constriction is elicited and in distribution of parasympathomimetic constriction within the first few generations of resistance bronchi. Our data also suggest that lung hyperinflation may lead to augmented airway contractile responses by shifting resting smooth muscle length toward optimum resting smooth muscle length.     

Enhancement of antibody production by growth factor addition in perfusion and hollow-fiber culture systems

The effects of the high-molecular-weight growth factors, transferrin and bovine serum albumin (BSA), on antibody production were analyzed quantitatively in continuous hollow-fiber cultivation over a period of 60 days. Transferrin enhanced cell growth but had no significant effect on the specific antibody production rate, whereas BSA significantly enhanced antibody production. The antibody production rate was increased 4- and 14-fold respectively by feeding BSA at 2 and 5 g L(-1) into the EC side of the system (the side connected to the cell-containing outer part of the hollow-fiber unit) compared with the production achieved without BSA. Addition of 5 g L(1) BSA into the IC side of the system (the side connected to the inner part of the hollow-fiber unit) resulted in a 2.5-fold increase in the antibody production rate. The effect of BSA was also analyzed using the perfusion culture system with a separation unit. When fresh medium containing either 2 or 5 g L(-1) BSA was fed into the reactor, both the specific growth rate and specific death rate increased, while the specific antibody production rate was increased 2- and 25-fold, respectively, by feeding BSA at these two concentrations compared with no addition. Comparing the two systems, the increase in the antibody production rate achieved with the hollow-fiber system was threefold greater than that in the perfusion culture system with the same concentration of BSA feeding. (c) 1995 John Wiley & Sons, Inc.     

On-line state recognition in a yeast fed-batch culture using error vectors

The physiological states with respect to cell growth and ethanol production in a yeast fed-batch culture expressed in linguistic form could be recognized on-line by fuzzy inferencing based on error vectors. The error vector was newly defined here in a macroscopic elemental balance equation. The physiological states for cell growth and ethanol production were characterized by error vectors using many experimental data from fed-batch cultures. Fuzzy membership functions were constructed from the frequency distributions of the error vectors and state recognition was performed by fuzzy inferencing. In particular, an unusual physiological state for a yeast cultivation, in which aerobic ethanol production was accompanied by very low cell growth, could be recognized accurately. According to the results of the state recognition, an energy parameter, the P/O ratio in the metabolic reaction model was adaptively estimated, and the cell growth was successfully evaluated with the estimated P/O. (c) 1995 John Wiley & Sons, Inc.     

Optimal production of glutathione by controlling the specific growth rate of yeast in fed-batch culture

The optimal of the specific growth rate was obtained with simple mathematical model in a yeast fed-batch cultures. The model was based on the mass balance around the fed-batch system and the relationship between the specific growth rate, mu, and the specific production rate of glutathione, rho(G). The optimal profile of mu was calculated as a bang-bang type, That is mu, should start from the maximum value, mu(max) and should be kept at mu(max); then mu should be switched to mu(c), which gives a maximum value of rho(G). It was proven from the maximum principle that switching was needed only once, with the switching time from mu(max) to mu(c) depending on the final required glutathione content. Finally, this ideal profile of mu for the maximum production of glutathione was realized by manipulating the substrates feed rate in the fed-batch culture. Using the extended Kalman filter and a programmed-controller/feedback-compensator (PF) system, mu could be controlled at the optimal profile obtained. As a result, the maximum production of glutathione was accomplished fairly successfully. However, further improvement in the controller performance for mu is desired. The control strategy employed here can be applied to other batch reaction processes.     

Regulation by induction of branched-chain 2-oxo acid dehydrogenase complex in clofibrate-fed rat liver.

The activity of branched-chain 2-oxo acid dehydrogenase complex increased 3.0-fold in liver of rats fed on 0.1%(w/w) clofibrate. Immunotitration experiments with antibodies against the constituent enzymes of the complex revealed that this increase resulted mainly from the increased amounts of only two(a decarboxylase and a lipoate acyltransferase) of three components of the complex and that the other component(dihydrolipoamide dehydrogenase) remained unchanged in its content, irrespective of clofibrate administration. The increases of both enzyme components were associated with increases in their mRNA levels which were estimated by in vitro translation with poly(A)+ RNA.     

A maximum production strategy of lysine based on a simplified model derived from a metabolic reaction network

The aim of this study is to develop a strategy for maximum production of a target product with a simplified model derived from a metabolic reaction network through an example of lysine production. Based on the model, a search for the optimal specific growth rate profile was conducted among the available conditions of batch fermentation based on the derived model, when the total fermentation time was fixed. The optimal specific growth rate was obtained as a boundary control: initially, the specific growth rate was maintained at a maximum value and was subsequently switched to a critical value giving the maximum specific production rate. To make the specific growth rate follow this optimal profile as accurately as possible in batch mode, first, an appropriate initial concentration of leucine was employed in the experiment. Second, the feeding strategy of leucine was further studied. The specific growth rate profile with feeding was closer to the optimal one and the amount of lysine produced at the final stage of fermentation was increased about twofold, compared to that in the batch fermentation. Finally, the strategy was summarized as an algorithm for general use of this method.     

Maximum production strategy for biodegradable copolymer P(HB-co-HV) in fed-batch culture of Alcaligenes eutrophus

A novel strategy for the maximum production of a biodegradable copolymer, poly(3-hydroxybutyric-co-hydroxyvaleric) acid, P(HB-co-HV), was developed, based on the kinetic parameters obtained from fed-batch culture experiments of Alcaligenes eutrophus. The effects of various culture conditions such as mole ratio of carbon:nitrogen in feed medium (C/N); total fatty acids concentrations; and addition ratio of fatty acids on cultivation properties such as the specific rates of cell formation, mu (h-1), P(HB-co-HV) production, rho[g.P(HB-co-HV)/g.cell/h], production yield from fatty acids [g.P(HB-co-HV)/g.fatty acid], and mole fraction of monomeric units in the copolymer [mol.(HV)/{mol.(HB) + mol.(HV)}], were investigated. When nitrogen supply was sufficient for cell growth; that is, C/N (mol.nitrogen atom/mol.carbon atom) was low, mu was high, but rho and the production yield were low, because fatty acids were used mainly for energy formation and anabolic reactions in the cells. On the other hand, when nitrogen supply was limited for cell growth-that is, C/N was high-rho was high. The highest value of rho was obtained when C/N was 75. As the mole ratio of valeric acid (VA) to butyric acid (BA) in the feed medium was increased, the mole fraction of HV units in P(HB-co-HV) increased linearly. When the ratio of BA to VA in the feed medium was kept at a constant value, but C/N was increased, the mole fraction of HV units decreased. In particular, when C/N was >12, the mole fraction of HV units decreased linearly as C/N increased. When VA was utilized as the sole carbon source and C/N was fixed at 4, P(HB-co-HV) with the highest mole fraction of HV units (67 mol%) was achieved. From these results, it was shown that both C/N and the mole ratio of BA to VA in the feed medium should be well controlled for an optimal production of P(HB-co-HV) with the desired value of the mole fraction of HV units. When the addition ratio of butyric acid was 50 wt% of total fatty acids, a maximum production strategy for P(HB-co-HV) was developed and realized experimentally, which was based on a model of the relationship between mu and rho.     

Optimization of agitation and aeration conditions for maximum virginiamycin production

To maximize the productivity of virginiamycin, which is a commercially important antibiotic as an animal feed additive, an empirical approach was employed in the batch culture of Streptomyces virginiae. Here, the effects of dissolved oxygen (DO) concentration and agitation speed on the maximum cell concentration at the production phase, as well as on the productivity of virginiamycin, were investigated. To maintain the DO concentration in the fermentor at a certain level, either the agitation speed or the inlet oxygen concentration of the supply gas was manipulated. It was found that increasing the agitation speed had a positive effect on the antibiotic productivity independent of the DO concentration. The optimum DO concentration, agitation speed and addition of an autoregulator, virginiae butanolide C (VB-C), were determined to maximize virginiamycin productivity. The optimal strategy was to start the cultivation at 450 rpm and to continue until the DO concentration reached 80%. After reaching 80%, the DO concentration was maintained at this level by changing the agitation speed, up to a maximum of 800 rpm. The addition of an optimal amount of the autoregulator VB-C in an experiment resulted in the maximal production of virginiamycin M (399 mg/l), which was about 1.8-fold those obtained previously. Received: 13 July 1998 / Received revision: 19 August 1998 / Accepted: 13 September 1998