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.

On-line estimation of biological variables during pH controlled lactic acid fermentations.

Indirect measurement of lactose, galactose, lactic acid, and biomass concentration from on-line sodium hydroxide weight measurements have been obtained for pure and mixed batch cultures of Streptococcus salivarius ssp. thermophilus 404 and Lactobacillus delbrueckii subsp. bulgaricus 398 conducted at controlled pH and temperature. Linear correlations were established between the equivalent sodium hydroxide concentration and the lactose (substrate), galactose and lactic acid (products) concentrations while nonlinear relationships were developed between biomass and lactic acid concentrations. These nonlinear relationships took into account the inhibitory effect of lactic acid on growth and acidification. The indirect measurements of biomass concentration were introduced into a nonlinear estimator of the state variables and of the specific growth and lactic acid production rates. Good agreement was found between estimated and measured biomass concentrations (error index ranging from 10.8% to 12.6%). The results showed the feasibility of on-line estimation of biomass concentration and of the specific kinetics from NaOH addition weight measurements and its applicability for monitoring lactic acid fermentations. Using off-line measurements of L(+) and D(-) lactic acid concentrations, the evolution of the concentration of each strain in mixed cultures was obtained from the relationships proposed for the mixed cultures. (c) 1994 John Wiley & Sons, Inc.

BIOESTIM: software for automatic design of estimators in bioprocess engineering.

This paper describes BIOESTIM, a software package devoted to on-line estimation in bioprocess engineering. BIOESTIM enables bioengineers automatically to design state and parameter estimators from a minimal knowledge of the process kinetics. Such estimators allow development of software sensors capable of coping with the lack of reliable instrumentation suited to real-time monitoring. The estimator building procedure through BIOESTIM starts up from a dynamical material balance model of the bioprocess. This model, supplied by the user, is next completed by other information with no requirement for numerical values: the user has only to specify available measurements, coupled reactions and the known yield coefficients. On the base of this knowledge, BIOESTIM proceeds to symbolic algebraic manipulations on the model in order to study estimation possibilities and check identifiability of yield coefficients. When the design of an estimator is possible, the corresponding equations are automatically generated. Moreover, these estimators are stored in a user-specified file which is automatically interfaced with a specialized simulation software including data treatment and numerical integration packages. Thus, the user can simulate the estimator performances under various operational conditions using available experimental measurements. A typical example dealing with microbial growth and biosynthesis reactions is given in order to illustrate the main functional capabilities of BIOESTIM. BIOESTIM has been designed and written in a modular fashion. The module dealing with estimators design makes use of symbolic computation; it is written in Mathematica and runs on every computer on which this language is available.

CAMBIO: software for modelling and simulation of bioprocesses.

CAMBIO, a software package devoted to bioprocess modelling, which runs on Apollo computers, is described. This software enables bioengineers to easily and interactively design appropriate mathematical models directly from their perception of the process. CAMBIO provides the user with a set of design symbols and mnemonic icons in order to interactively design a functional diagram. This diagram has to exhibit the most relevant components with their related interactions through biological and physico-chemical reactions. Then, CAMBIO automatically generates the dynamical material balance equations of the process in the form of an algebraic-differential system by taking advantage of the knowledge involved in the functional diagram. The model may be used for control design purpose or completed by kinetics expressions with a view to simulation. CAMBIO offers facilities to generate a simulation model (for coding of kinetics, introducing auxiliary variables, etc.). This model is automatically interfaced with a specialized simulation software which allows an immediate visualization of the process dynamical behaviour under various operational conditions (possibly involving feedback control strategies). An example of an application dealing with yeast fermentation is given.

On-line prediction of fermentation variables using neural networks.

This article presents an introduction to the use of neural network computational algorithms for the dynamic modeling of bioprocesses. The dynamic neural model is used for the prediction of key fermentation variables. This relatively hew method is compared with a more traditional prediction technique to judge its performance for prediction. Illustrative simulation results of a continuous stirred tank fermentor are used for this comparison. It is shown that neural network models are accurate with a certain degree of noise immunity. They offer the distinctive ability over more traditional methods to learn very naturally complex relationships without requiring the knowledge of the model structure.

Origin and fate of rat plasma cholesterol in vivo. Modelling of cholesterol movements between plasma and organs.

A cholesterol system model was developed in the rat following a single injection of red cells containing free (unesterified) [3H]cholesterol. The radioactivity of free and esterified cholesterol in the different parts of the system was measured during the 48 h following tracer introduction. The model consisted of seven compartments (red cell free cholesterol, plasma and liver free and esterified cholesterol, total cholesterol in the rapidly and slowly exchangeable carcass pools). The model was validated by the similarity between simulated and experimental values during the 48 h following tracer introduction. Both the fractional rate of cholesterol esterification in the plasma (0.44 h-1) and liver (0.01 h-1) and the fractional exchange rate of free cholesterol from the plasma towards the various organs (particularly 3 h-1 towards the liver for a total of 7 h-1) can be estimated with this model. The results show that cholesterol movements between the plasma and the different organs take place mainly through intense free cholesterol exchanges, resulting in a low net flux.

[Effect of subinhibitory concentrations of antibiotics on the growth level of bacteria]. / Effet des concentrations subinhibitrices d'antibiotiques sur le taux de croissance des bactéries.

The effect of subinhibitory concentrations of 5 antibiotics on the growth rate of 2 bacteria (Staphylococcus aureus and Escherichia coli) has been studied. Chloramphenicol, dibekacin, netilmicin and nalidixic acid have a direct effect on the growth rate. Apparently, aminoglycosides and nalidixic acid have an accompanying effect on the affinity for the energizing substrate. Amoxicillin does not seem to be concerned by this 2 mechanisms. The interest of the estimation of the growth rate by an adaptative algorithm has been pointed out.

The measurement in vivo of the rate of unesterified cholesterol exchange between rat plasma and erythrocytes.

In order to investigate the rate of unesterified cholesterol exchange between plasma and erythrocytes in vivo, cholesterol labelling in rats was achieved in one of the following ways: intravenous injection of cholesterol-labelled erythrocytes, subcutaneous injection of labelled acetate, feeding of labelled cholesterol. The specific activity of the unesterified cholesterol was measured at intervals up to 24 h and a kinetic analysis of the data was performed. It assumes that both the cholesterol in the erythrocytes and the unesterified cholesterol in the plasma were homogeneous pools. The rate constants obtained for the movements of unesterified cholesterol from erythrocytes to plasma and from plasma to erythrocytes were not significantly different in the three labelling conditions (mean values: 0.26 and 1.5 h-1, respectively).