Sensitivity analysis and reduction of a dynamic model of a bioproduction of fructo-oligosaccharides.

Starting from a relatively detailed model of a bioprocess producing fructo-oligosaccharides, a set of experimental data collected in batch and fed-batch experiments is exploited to estimate the unknown model parameters. The original model includes the growth of the fungus Aureobasidium pullulans which produces the enzymes responsible for the hydrolysis and transfructosylation reactions, and as such contains 25 kinetic parameters and 16 pseudo-stoichiometric coefficients, which are not uniquely identifiable with the data at hand. The aim of this study is, therefore, to show how sensitivity analysis and quantitative indicators based on the Fisher information matrix can be used to reduce the detailed model to a practically identifiable model. Parametric sensitivity analysis can indeed be used to progressively simplify the model to a representation involving 15 kinetic parameters and 8 pseudo-stoichiometric coefficients. The reduced model provides satisfactory prediction and can be convincingly cross validated.

Optimization and robustness analysis of hybridoma cell fed-batch cultures using the overflow metabolism model.

The maximization of biomass productivity in fed-batch cultures of hybridoma cells is analyzed based on the overflow metabolism model. Due to overflow metabolism, often attributed to limited oxygen capacity, lactate and ammonia are formed when the substrate concentrations (glucose and glutamine) are above a critical value, which results in a decrease in biomass productivity. Optimal feeding rate, on the one hand, for a single feed stream containing both glucose and glutamine and, on the other hand, for two separate feed streams of glucose and glutamine are determined using a Nelder-Mead simplex optimization algorithm. The optimal multi exponential feed rate trajectory improves the biomass productivity by 10 % as compared to the optimal single exponential feed rate. Moreover, this result is validated by the one obtained with the analytical approach in which glucose and glutamine are fed to the culture so as to control the hybridoma cells at the critical metabolic state, which allows maximizing the biomass productivity. The robustness analysis of optimal feeding profiles obtained with different optimization strategies is considered, first, with respect to parameter uncertainties and, finally, to model structure errors.

Application of super-twisting observers to the estimation of state and unknown inputs in an anaerobic digestion system.

This paper presents the estimation of the unknown states and inputs of an anaerobic digestion system characterized by a two-step reaction model. The estimation is based on the measurement of the two substrate concentrations and of the outflow rate of biogas and relies on the use of an observer, consisting of three parts. The first is a generalized super-twisting observer, which estimates a linear combination of the two input concentrations. The second is an asymptotic observer, which provides one of the two biomass concentrations, whereas the third is a super-twisting observer for one of the input concentrations and the second biomass concentration.

Nitrogen-backboned modeling of wine-making in standard and nitrogen-added fermentations.

Nitrogen has a strong impact on the key bio-mechanisms involved during the grape-must fermentation but also on the synthesis of flavour markers determining the aromatic profile of the wine. This paper first presents a consistent dynamical mass balance model describing the main physiological phenomena implied in standard batch fermentations, i.e. consumption of sugar and nitrogen and synthesis of ethanol. It also includes nitrogen compounds such as hexose transporters. Moreover, a common practice in wine-making is the addition of nitrogen during the fermentation in order to boost and shorten the process duration. A tractable representation of this boost effect has therefore been developed as an extension of the first model. It is apparent that yeast makes a different use of nitrogen depending on the fermentation stage at which the addition is effected, balancing the regrowth of biomass and the synthesis of supplementary hexose transporters. These models have been validated in line with experimental evidence deduced from extensive experimental studies.

Dynamic metabolic models of CHO cell cultures through minimal sets of elementary flux modes.

The concept of Elementary Flux Modes (EFMs) has been of central importance in a number of studies involving the analysis of metabolism. In Provost and Bastin (2007) this concept is used to translate the metabolic networks of the different phases of CHO cell cultures into macroscopic bioreactions linking extracellular substrates to products. However, a critical issue concerns the calculation of these elementary flux vectors, as their number combinatorially increases with the size of the metabolic network. In this study, a detailed metabolic network of CHO cells is considered, where the above-mentioned combinatorial explosion makes the computation of the elementary flux modes impossible. To alleviate this problem, a methodology proposed in Jungers et al. (2011) is used to compute a decomposition of admissible flux vectors in a minimal number of elementary flux modes without explicitly enumerating all of them. As a result, a set of macroscopic bioreactions linking the extracellular measured species is obtained at a very low computational expense. The procedure is repeated for the several cell culture phases and a global model is built using a multi-model approach, which is able to successfully predict the evolution of experimental data.

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.

Robust control of the activated sludge process.

In this work, a robust control strategy is proposed for maintaining the oxygen concentration in the aerobic tank and the pollutant, i.e., ammonium, nitrate, nitrite, concentrations at acceptable levels in the effluent water at the outlet of the activated sludge process. To this end, the Activated Sludge Model no. 1 (ASM1) is first reduced using biological arguments and a singular perturbation method, and a simplified model of the secondary settler is included. In contrast with previous studies that make use of piecewise linear models, an average operating point is evaluated using available data (here data from the COST Action 624) and the reduced-order model is linearized around it using standard techniques. Finally, a H(2) robust control strategy acting on the oxygen injection and the recirculated flow rate is designed and tested in simulation.

Continuous-discrete interval observers for monitoring microalgae cultures.

Algorithms estimating unmeasured component concentrations play a key role in bioprocess applications where only a few on-line measurements are usually available. In this article, interval observers are designed to provide guaranteed intervals for the key components involved in cultures of microalgae. In contrast with most of the published studies focusing on continuous-time measurements, this study considers discrete-time measurements with possibly long and irregular sampling and defines predictors based on model equations and state transformations to ensure the enclosure of the state variables between two measurement times. The methods are validated with experimental data where the remaining inorganic nitrogen and the microalgal internal quota are estimated.

Modeling and numerical simulation of secondary settlers: a method of lines strategy.

In this paper, attention is focused on a parabolic partial differential equation (PDE) modeling sedimentation in a secondary settler and the proper formulation of the problem boundary conditions (i.e., the conditions prevailing at the feed, clear water and sludge outlets). The presence of a diffusion term in the equation not only allows the reproduction of experimental observations, as reported in a number of works, but also makes the numerical solution of the initial-boundary value problem significantly easier than the original conservation law (which is a nonlinear hyperbolic PDE problem requiring advanced numerical techniques). A Method of Lines (MOL) solution strategy is then proposed, based on the use of finite differences or spectral methods, and on readily available time integrators. The efficiency and flexibility of the general procedure are demonstrated with various numerical simulation results.

On a general model structure for macroscopic biological reaction rates.

Macroscopic modelling of bioprocesses requires the determination of a biological reaction scheme and a kinetic model. The a priori selection of an appropriate kinetic model structure is usually made difficult by the lack of detailed bioprocess knowledge and the profusion of apparently similar biological kinetic laws. Moreover, parameter identification is made arduous and time-consuming by the strong non-linearities involved in kinetic laws. In most cases, these kinetic structures are non-linearizable and no first parameter estimation can be deduced easily. In order to avoid such identification problems, Bogaerts et al. [Bogaerts, Ph., Castillo, J., Hanus, R., 1999. A general mathematical modelling technique for bioprocesses in engineering applications. Syst. Anal. Model. Simul. 35, 87-113] have developed a general linearizable kinetic structure which allows the representation of activation and/or inhibition effects of each component in the culture. This paper further generalizes this structure in order to improve the way saturation effects are taken into account, and in turn, improve the biological interpretation of the model parameters. The main advantage of the proposed structure lies in an associated systematic estimation procedure. The usefulness of the proposed model is tested with simulated as well as with experimental data.

On a systematic procedure for the predetermination of macroscopic reaction schemes.

Macroscopic modeling of biological cell cultures involves two major steps: (a) the selection of a reaction scheme and (b) the determination of the reaction kinetics. The first step is usually accomplished based on prior knowledge, experimental investigation and trials and errors. This procedure can be time consuming, and more importantly, can lead to the selection of a reaction scheme omitting some important reaction pathways, or at the opposite, incorporating too many details (at least considering the data at hand and the modeling objectives). This paper addresses this modeling problem, and aims at the development of a method for systematically evaluating (i.e. setting up and comparing) all potential reaction schemes, based on a set of measured components, and satisfying structural identifiability properties. One of the main features of the method is that the yield (or pseudo-stoichiometric) coefficients can be estimated independently of the kinetics. The method is illustrated with simulation results and an experimental case study.

A general model of reaction kinetics in biological systems.

Dynamic mathematical models in biotechnology require, besides the information about the stoichiometry of the biological reaction system, knowledge about the reaction kinetics. Modulation phenomena like limitation, inhibition and activation occur in different forms of competition with the key enzymes responsible for the respective metabolic reaction steps. The identification of a priori unknown reaction kinetics is often a critical task due to the non-linearity and (over-) parameterization of the model equations introduced to account for all the possible modulation phenomena. The contribution of this paper is to propose a general formulation of reaction kinetics, as an extension of the Michaelis-Menten kinetics, which allows limitation/activation and inhibition effects to be described with a reduced number of parameters. The versatility of the new model structure is demonstrated with application examples.

Software sensors for bioprocesses.

State estimation is a significant problem in biotechnological processes, due to the general lack of hardware sensor measurements of the variables describing the process dynamics. The objective of this paper is to review a number of software sensor design methods, including extended Kalman filters, receding-horizon observers, asymptotic observers, and hybrid observers, which can be efficiently applied to bioprocesses. These several methods are illustrated with simulation and real-life case studies.