3BIO-BioControl Team Publications

Peer-reviewed journal articles
 

Articles dans des revues avec comité de lecture

2022

A systematic elementary flux mode selection procedure for deriving macroscopic bioreaction models from metabolic networks

Elementary flux modes (EFMs) are an important concept in metabolic pathway analysis and for the derivation of macroscopic dynamic models. However, the computation of elementary flux vectors is facing combinatorial explosion with the size of the metabolic network, which hinders widespread application. This study proposes a systematic elementary flux mode reduction procedure to derive reduced-order dynamic models starting from an initial set of EFMs either generated by complete enumeration or subset selection. The procedure proceeds in several steps, including geometric and optimization-based criteria. The methodology ends up with a macroscopic bioreaction scheme with a reaction number smaller than that of the measured species, and shows very satisfactory prediction results, as illustrated with data of batch cultures of CHO-320 cells.

Hybrid Dynamic Models of Bioprocesses Based on Elementary Flux Modes and Multilayer Perceptrons

The derivation of minimal bioreaction models is of primary importance to develop monitoring and control strategies of cell/microorganism culture production. These minimal bioreaction models can be obtained based on the selection of a basis of elementary flux modes (EFMs) using an algorithm starting from a relatively large set of EFMs and progressively reducing their numbers based on geometric and least-squares residual criteria. The reaction rates associated with the selected EFMs usually have complex features resulting from the combination of different activation, inhibition and saturation effects from several culture species. Multilayer perceptrons (MLPs) are used in order to undertake the representation of these rates, resulting in a hybrid dynamic model combining the mass-balance equations provided by the EFMs to the rate equations described by the MLPs. To further reduce the number of kinetic parameters of the model, pruning algorithms for the MLPs are also considered. The whole procedure ends up with reduced-order macroscopic models that show promising prediction results, as illustrated with data of perfusion cultures of hybridoma cell line HB-58.

Macroscopic Modeling of Intracellular Trehalose Concentration in Saccharomyces cerevisiae Fed-batch Cultures

This paper describes the extension of a baker's yeast growth model to account for the intracellular trehalose storage and mobilization. Trehalose is a reserve carbohydrate that is accumulated and converted back to intracellular glucose when the yeast cells face certain stresses. This is modeled by a new macroscopic reaction, which is coupled to an existing macroscopic reaction scheme describing the coordinated uptake of glucose and ammonium by the yeast cells. The dynamics of the trehalose concentration is described by a delay differential equation as the available experimental data used to fit the model exhibits a time-delayed correlation between trehalose storage and glucose uptake as well as a time-delayed correlation between trehalose mobilization and ethanol respiration phases. The proposed extension contains 6 parameters of which 5 are estimated via nonlinear least squares identification. The proposed model predicts accurately the dynamics of trehalose storage and mobilization and can be used to optimize the intracellular trehalose accumulation in Saccharomyces cerevisiae, which is valuable for obtaining reinforced yeast cells, able to better withstand drying operations.

A Simulation Study on Model-Based Optimization of Intracellular Trehalose Accumulation in Saccharomyces cerevisiae Fed-Batch Cultures

Special Issue: Mathematical Modeling and Control of Bioprocesses

2021

Discopolis 2.0: A new recursive version of the algorithm for uniform sampling of metabolic flux distributions with linear programming

How to Tackle Underdeterminacy in Metabolic Flux Analysis? A Tutorial and Critical Review

Metabolic flux analysis is often (not to say almost always) faced with system underdeterminacy. Indeed, the linear algebraic system formed by the steady-state mass balance equations around the intracellular metabolites and the equality constraints related to the measurements of extracellular fluxes do not define a unique solution for the distribution of intracellular fluxes, but instead a set of solutions belonging to a convex polytope. Various methods have been proposed to tackle this underdeterminacy, including flux pathway analysis, flux balance analysis, flux variability analysis and sampling. These approaches are reviewed in this article and a toy example supports the discussion with illustrative numerical results.

Selection of a minimal suboptimal set of EFMs for dynamic metabolic modelling

Mathematical modelling supports the understanding of basic biological mechanisms and is the basis for bioprocess simulation, prediction, control and optimization. Dynamic macroscopic models can be derived from the concept of elementary flux modes (EFMs), which provide a comprehensive representation of all possible pathways through a metabolic network. As the number of EFMs drastically increases with the size of the metabolic network, a procedure to reduce the number of EFMs and select the most informative ones is required. For this purpose, this study proposes a methodology to select a minimal suboptimal set of elementary flux modes allowing the development of reduced macroscopic models. The algorithm is divided into two steps. First, the concept behind the cosine-similarity algorithm is extended for a large number of EFMs to cut the initial set by removing all the collinear modes. Next, the algorithm is used to extract only the most informative modes from the reduced set by means of a series of optimization problems. The algorithm performance is illustrated with datasets from hybridoma cultures in batch and perfusion modes, and two metabolic networks with different levels of description.

Discopolis 2.0: A new recursive version of the algorithm for uniform sampling of metabolic flux distributions with linear programming

Metabolic flux values are subject to equality (e.g., mass balances, measured fluxes) and inequality (e.g., upper and lower flux bounds) constraints. The system is generally underdetermined, i.e. with more unknown fluxes than equations, and all the admissible solutions belong to a convex polytope. Sampling that polytope allows subsequently computing marginal distributions for each metabolic flux. We propose a new version of the DISCOPOLIS algorithm (DIscrete Sampling of COnvex POlytopes via Linear program Iterative Sequences) that provides the same weight to all the samples and that approximates a uniform distribution thanks to a recursive loop that computes variable numbers (called grid points) of samples depending on the fluxes that have already been fixed in former iterations. The method is illustrated on three different case studies (with 3, 95 and 1054 fluxes) and shows interesting results in terms of flux distribution convergence and large ranges of the marginal flux distributions. Three consistent criteria are proposed to choose the optimal maximum number of grid points.

2020

Modeling the Molecular Impact of SARS-CoV-2 Infection on the Renin-Angiotensin System

SARS-CoV-2 infection is mediated by the binding of its spike protein to the angiotensin-converting enzyme 2 (ACE2), which plays a pivotal role in the renin-angiotensin system (RAS). The study of RAS dysregulation due to SARS-CoV-2 infection is fundamentally important for a better understanding of the pathogenic mechanisms and risk factors associated with COVID-19 coronavirus disease and to design effective therapeutic strategies. In this context, we developed a mathematical model of RAS based on data regarding protein and peptide concentrations; the model was tested on clinical data from healthy normotensive and hypertensive individuals. We used our model to analyze the impact of SARS-CoV-2 infection on RAS, which we modeled through a downregulation of ACE2 as a function of viral load. We also used it to predict the effect of RAS-targeting drugs, such as RAS-blockers, human recombinant ACE2, and angiotensin 1-7 peptide, on COVID-19 patients; the model predicted an improvement of the clinical outcome for some drugs and a worsening for others. Our model and its predictions constitute a valuable framework for in silico testing of hypotheses about the COVID-19 pathogenic mechanisms and the effect of drugs aiming to restore RAS functionality.

Adaptive flux variability analysis of HEK cell cultures

Measured external fluxes impose constraints to under-determined metabolic networks that narrow the internal flux intervals obtained using Flux Variability Analysis. Nevertheless, these constraints often lead to systems that do not admit a feasible solution. Measurement noise and data smoothing are among the sources of uncertainties that can cause system infeasibility. These constraints are classically released using interval representation of fluxes. This study investigates the use of Adaptive Flux Variability Analysis (AFVA), which allows determining a minimal coefficient of variation of the external fluxes along the time course of the experiment. Especially, AFVA is applied to a medium-size metabolic network and a rich dataset relative to HEK-293 cells cultured in batch, encompassing all 20 amino acids and less commonly measured metabolites, such as urea and pyruvate. AFVA appears as an effective tool for metabolic flux analysis. The impact of data-smoothing and the information provided by the cell growth are thoroughly analyzed.

2019

FBA-based simulator of Saccharomyces cerevisiae fed-batch cultures involving an internal unbalanced metabolite

A dynamic macroscopic simulator based on Flux Balance Analysis (FBA) is proposed to predict the dynamics of biomass growth, substrate consumption (glucose and ammonium) and ethanol production in S. cerevisiae fed-batch cultures. It is based on a metabolic network containing the main metabolism of the yeast, an objective cost function aiming at maximizing the biomass growth, different inequalities corresponding to some biological assumptions such as glucose overflow metabolism and inequalities which link the fluxes to models of substrate uptake rates. Since it was not possible to accurately correlate the input fluxes with only the extracellular species concentration, a new variable is introduced in the uptake rate models using the information at intracellular level. We first determine the dynamics corresponding to the intracellular metabolite, namely alpha-ketoglutarate, and, in a second part, this new information is used for modelling the input flux rates. Secondly, all the information is integrated in a set of mass balances for building a simulator based only on the initial conditions of each species and the feeding rate. It is validated with direct and cross-validation. This model allows, on the one hand, reproducing the dynamics of extracellular species and, on the other hand, describing the accumulation of alpha-ketoglutarate.

FBA-based prediction of biomass and ethanol concentration time profiles in: Saccharomyces cerevisiae FED-bath cultures

A Flux Balance Analysis (FBA)-based dynamical model is proposed for predicting biomass and ethanol concentration time profiles in Saccharomyces cerevisiae fed-batch cultures, with glucose and ammonium uptake rates as inputs. It is based on a metabolic network compiling the necessary internal fluxes for reproducing respiratory as well as respiro-fermentative metabolisms. While the objective cost function classically accounts for biomass growth maximization, additional linear constraints are used to reproduce overflow metabolism phenomena. New conditional equality constraints are introduced in the FBA linear programs to account for variable biomass composition (based on protein mass fraction identification with or without ammonium feeding). The proposed FBA-based model contains only 7 parameters which are estimated with the experimental data. A two-step procedure for separately solving the FBA linear programs and the macroscopic mass balance ODEs significantly lowers the computational load for parameter identification. Direct and leave-one-out cross-validation results are provided.

Determining a unique solution to underdetermined metabolic networks via a systematic path through the Most Accurate Fluxes

Metabolic Flux Analysis (MFA) and Flux Balance Analysis (FBA) often lead to underdetermined problems in the sense that there are more unknown fluxes in the metabolic network than the number of available equations which represent balanced metabolites and measured fluxes. Even the additional inequality constraints, e.g. flux positivity, and/or the use of an objective function in FBA do not allow obtaining a unique solution in many cases. This contribution aims at determining a simple, systematic and computationally efficient algorithm for obtaining a unique solution based on the iterative determination of the Most Accurate Fluxes (MAF). A measure of accuracy is introduced and the systematic algorithm is proposed and illustrated on a case study aiming at the determination of unique dynamic flux values within hybridoma cells. It is also shown that the MAF distribution is similar to the mean values obtained from a uniform sampling of admissible solutions.

Adaptive flux variability analysis: A tool to deal with uncertainties

Underdetermined metabolic networks are usually investigated using Flux Variability Analysis (FVA) under the pseudo-steady state assumption of the internal metabolites. When a dynamic overview of the flux map is sought, the time variation of the cell uptake and excretion rates is deduced from extracellular dynamic mass balances and smoothing of the measurement data of the time evolution of the extracellular concentrations. Nevertheless, the resulting system of equations does not always admit a feasible solution under these constraints. Indeed, measurement data is affected by noise, whose processing (smoothing, etc) always entails some subjective user choices, and the network itself might not be perfectly suited to explain the several culture phases. To alleviate these adverse effects, the constraints can be relaxed by introducing coefficients of variation of the external fluxes, and by considering an interval representation of the fluxes. This work presents a systematic method to determine these coefficients of variation, along the time course of the culture, leading to an adaptive scheme where the coefficients are set to the tightest bounds. The methodology is applied to experimental data of cultures of hybridoma in batch and perfusion modes and compared to previously published results.

DISCOPOLIS : an algorithm for uniform sampling of metabolic flux distributions via iterative sequences of linear programs

Mathematical modeling and dynamic analysis of complex biological systems

2018

Dynamic flux balance analysis for predicting biomass growth and ethanol production in yeast fed-batch cultures

In this study, a metabolic flux analysis (MFA) is firstly applied, at each time instant, for determining the range of admissible fluxes based on glucose and ammonium uptake rates and ethanol production rate estimated from measured concentrations in Saccharomyces cerevisiae fed-batch cultures. Given the similarity between the upper bound of the biomass production flux and its estimation through concentration measurements, a flux balance analysis (FBA), aiming at maximizing the biomass growth, is proposed and allows narrowing the admissible flux ranges within the metabolic network. Finally, after withdrawing the information corresponding to the ethanol production rate, original inequality constraints describing overflow metabolism of glucose are added to the FBA linear program in order to compensate for the lack of information regarding ethanol production. This final FBA model allows predicting biomass growth and ethanol production rates, which are consistent with the experimental measurements.

2017

From MFA to FBA: Defining linear constraints accounting for overflow metabolism in a macroscopic FBA-based dynamical model of cell cultures in bioreactor

Macroscopic dynamical models of cell cultures in bioreactor are made of sets of ODEs representing the mass balances of the main macroscopic species (biomass, main substrates and metabolites). They can be coupled to a Flux Balance Analysis (FBA) linear program whose solution gives metabolic flux values at each time instant. The linear constraints used in this linear program are made of positivity constraints for the fluxes, equalities which link the fluxes to simple macroscopic models of the substrate uptake rates and a set of equalities and inequalities corresponding to some biological assumptions. In this paper, a methodology is proposed to help defining this latter set of linear constraints, with a special focus on overflow metabolism description. It is shown how these linear constraints, together with the objective cost function to be used in the linear program, can be derived from a preliminary Metabolic Flux Analysis (MFA) and a careful comparison of the admissible metabolic flux intervals obtained either using both input and output flux measurements or using only input flux measurements. Finally, a method is proposed for estimating the dynamical model output uncertainties resulting from the intervals of admissible fluxes. In a case study made of hybridoma cell batch and fed-batch cultures, it is shown how to model overflow metabolism on both glucose and glutamine thanks to inequality constraints. The linear program corresponding to a FBA problem is then used in a macroscopic dynamical model which is able to reproduce biomass, substrates and metabolites concentration time profiles in direct and cross validation.

2016

A methodology for building a macroscopic FBA-based dynamical simulator of cell cultures through flux variability analysis

A dynamical FBA-based simulator of hybridoma cell fed-batch cultures predicting the dynamics of biomass growth, substrate consumption (glucose and glutamine), metabolites production (lactate, ammonium and alanine) and associate intracellular metabolism based on a simplified metabolic network is proposed. A preliminary comparison between the range of admissible flux distribution obtained based on all available measurements (the two substrates uptake rates and the three metabolite production rates) and based on only part of them (only the two substrates uptake rates) is performed to deal with the usual problem of system underdetermination in constraint-based modeling context. This comparative flux variability analysis allows the objective identification of some additional constraints (to be used in the final FBA-based simulator) so as to obtain similar admissible flux intervals in both cases. Moreover, the proposed approach legitimates the cost criterion used for the linear optimization, i.e. cell growth maximization. This methodology is validated on experimental data of two fed-batch cultures and cross validated on a batch culture of hybridoma cells HB-58. The flux distribution results are in agreement with overflow metabolism description available in literature.

Design of a Robust Lipschitz Observer-Application to monitoring of culture of micro-algae Scenesdesmus obliquus

In this study, the application of Lipschitz observers to the monitoring of cultures of micro-algae in photo-bioreactors is investigated. To design the observer, the dynamic model has to be structured into an observable linear part and a nonlinear Lipschitz part. A systematic method is proposed for the definition of the linear part, so as to ensure that it is stable and observable. The observer is tested in a real-life application, namely cultures of micro-algae Scenesdesmus obliquus, where the internal quota has to be estimated from either biomass measurements only or biomass and medium substrate concentrations. The Lipschitz observer shows robust performance, as compared to the extended Kalman filter.

DYNAMIC MICROORGANISM GROWTH MODELING FOR SHELF LIFE PREDICTION: APPLICATION TO COOKED AND BRINED SHRIMPS

Listeria monocytogenes growth data in cooked and brined shrimps under different storage temperatures (0°C, 5°C, 8°C, 15°C and 25°C) were selected from Combase (Dalgaard and Jørgensen, 2000) to develop a dynamic model for shelf life prediction. Based on a multi-step parameter identification procedure, the Baranyi model was fitted for the growth curves of L. monocytogenes, coupled with the Ratkowsky square root model and a sigmoidal function as secondary models for the temperature dependency of the maximum specific growth rate and the maximum cell density respectively. Uncertainty on the prediction of the global growth model was analyzed and the 95% confidence intervals of the predicted microorganism concentration time profiles were determined. Based on these latter, shelf life estimation was 42-53 days, 9-11 days, 3-4 days at 8°C, 15°C and 25°C respectively according to the upper limit of L. monocytogenes in ready-to-eat products, 100 cfu/g. These results are in agreement with those presented in (Dalgaard and Jørgensen, 2000), which illustrates the shelf life prediction abilities of the proposed dynamic growth model.

FROM MFA TO FBA: LEGITIMATING OBJECTIVE FUNCTION AND LINEAR CONSTRAINTS

A careful analysis of the admissible metabolic flux intervals (determined from linear programs) obtained with detailed (input and output) or limited (only input) flux measurements is proposed in a case study made of a fed-batch culture of hybridoma cells. It is shown how a cost function in FBA and additional linear constraints on the fluxes can be legitimated and efficiently introduced so as to recover admissible flux intervals based on limited external measurements which are similar to the ones based on all the available measurements. A way to model overflow metabolism on both glucose and glutamine thanks to only two inequality constraints is proposed.

2015

Systematic methodology for bioprocess model identification based on generalized kinetic functions

This study presents a new systematic methodology for kinetic model identification on the basis of available experimental measurements. In a first step, a general kinetic model [Syst. Anal. Model. Simul. 35 (1999) 87-113] is identified, which allows, on the one hand, capturing the activation and/or inhibition effects of any component involved in the reaction and, on the other hand, identifying all the parameters based on a simple linear regression. This circumvents the tedious problems of choosing the kinetic structure and providing initial parameter values on a trial-and-error basis. In a second step, the general kinetic model can be easily transformed into the general extended Monod formalism. The global identification of the nonlinear model is finally performed based on the results of the previous steps. The model and the experimental field (fed-batch culture experiments using hybridoma cell line HB-58) presented in Amribt et al. [Biochem. Eng. J. 70 (2013) 196-209] are used as case study to underline the advantages of this strategy for the global identification of nonlinear models. The proposed systematic procedure leads to the identification of a model structure with similar complexity but whose parameter values present lower variation coefficients. The identified model successfully reproduces the dynamics associated with substrates consumption (glucose and glutamine), metabolites production (lactate and ammonia) and cell growth.

Extended and Unscented Kalman Filter design for hybridoma cell fed-batch and continuous cultures

In order to mantain hybridoma cell cultures in optimal operating conditions, on-line measurements of glutamine and glucose concentrations are required, implying the availability of probes, which are expensive and with poor durability. A way to overcome this problem is to design software sensors. In this work, both Extended and Unscented Kalman Filters are developed in order to estimate glucose and glutamine concentrations, based on biomass, lactate and ammonia on-line measurements. System observability conditions are first examined. The performances of both software sensors are analyzed with simulations of hybridoma cell cultures in fed-batch and continuous bioreactor operating modes. Three different tests are conducted in order to compare the performance of both observers: continuous culture with constant feeding profile, fed-batch culture with both constant and exponential feeding profiles. Also, two different sets of parameters are investigated: the ones obtained by using the least-squares method in order to minimize the error between model predictions and experimental measurements, and the ones which are modified by minimizing a cost function combining the usual least-squares criterion with a state estimation sensitivity criterion.

Macroscopic modelling of intracellular reserve carbohydrates production during Baker's yeast cultures

An extension of the model by Richelle et al. (2014a) is developed to describe the reserve carbohydrates metabolism during yeast cultures. The model parameters were obtained via nonlinear least squares identification. It is validated with experimental data and successfully predicts the dynamics of accumulation and mobilization of trehalose and glycogen during all periods of cultures, even in crossvalidation. This extension, on the one hand, allows the quantitative description of the storage carbohydrates metabolism in yeast cultures; on the other hand, it will be valuable for the determination of culture conditions aiming at maximizing yeast production while guaranteeing the accumulation required amounts of trehalose and glycogen.

Macroscopic modelling of bioethanol production from potato peel wastes in batch cultures supplemented with inorganic nitrogen

Inorganic nitrogen supplementation is commonly used to boost fermentation metabolism in yeast cultures. However, an excessive addition can induce an opposite effect. Hence, it is important to ensure that the ammonia supplemented to the culture leads to an improvement of the ethanol production while avoiding undesirable inhibition effects. To this end, a macroscopic model describing the influence of ammonia addition on Saccharomyces cerevisiae metabolism during bioethanol production from potato peel wastes has been developed. The model parameters are obtained by a simplified identification methodology in five steps. It is validated with experimental data and successfully predicts the dynamics of growth, substrate consumption (ammonia and fermentable sugar sources) and bioethanol production, even in cross validation. The model is used to determine the optimal quantity of supplemented ammonia required for maximizing bioethanol production from potato peel wastes in batch cultures.

State estimation and predictive control of fed-batch cultures of hybridoma cells

Fed-batch cultures of hybridoma cells are commonly used for the production of monoclonal antibodies (MAb). In this study, a simple macroscopic model of the cell culture is used, which is based on the overflow metabolism paradigm. This allows to specify optimal culture conditions, and the natural formulation of a nonlinear model predictive control strategy (NMPC). As not all the component concentrations are available for measurement, system observability is analyzed, and an unscented Kalman filter (UKF) is designed, which provides satisfactory estimates of glucose and glutamine concentrations. Robustness of the NMPC scheme is investigated, as well as the combined UKF+NMPC scheme, through a minimax robust version and the closed-loop system.

2014

Off-line optimization of baker's yeast production process

A macroscopic model describing the influence of nitrogen on a fed-batch baker[U+05F3]s yeast production process was used for the determination of optimal operating conditions in the sense of a production criterion. To this end, two different approaches were used: a control vector parameterization approach with mesh refinement and an approach based on the mathematical analysis of optimal operating policy (semi-analytical approach). The results of the two approaches lead to the determination of similar optimal operation conditions, which have been implemented for a new experimental phase. Moreover, these optimal conditions are in agreement with the profiles obtained by industrial manufacturers through an empirical optimization of the process (trial and error method). The model predictions are in good accordance with experimental data. This conclusion was supported by an uncertainty analysis on the model outputs with respect to the parameter estimation errors. © 2014 Elsevier Ltd.

Macroscopic modelling of baker's yeast production in fed-batch cultures and its link with trehalose production

A macroscopic model describing the influence of nitrogen on a fed-batch baker's yeast production process is proposed. First, on the basis of a set of biological reactions, inspired by the model of Sonnleitner and Käppeli (1986), a model in which the nitrogen and glucose consumption are coordinated is proposed. Second, an attempt of estimating trehalose concentration in yeast cells through an extension of this model is presented. The model parameters are obtained via a non-linear least squares identification. It is validated with experimental data and successfully predicts the dynamics of growth, substrate consumption (nitrogen and carbon sources) and metabolite production (ethanol and trehalose). This model allows, on the one hand, quantitatively describing the link between nitrogen and glucose consumption in yeast cultures and, on the other hand, will be valuable for the determination of culture conditions aiming at maximizing yeast productivity while guaranteeing the accumulation of a required amount of trehalose. © 2013 Elsevier Ltd.

Robust nonlinear state estimation of bioreactors based on H∞ hybrid observers

This paper proposes a robust nonlinear observer for bioreactors combining the classical asymptotic observer and a nonlinear Luenberger-like observer. The resulting hybrid observer considers a new definition of the hybridization parameter which reflects the kinetic model confidence. The nonlinear observer is tuned on the basis of robust H-infinity approach and the differential-algebraic representation (DAR) of nonlinear systems. A simulated case study concerning fed-batch animal cell cultures is presented to demonstrate the potentials and advantages of the proposed approach for state estimation of bioreactors. © 2013 Elsevier Ltd.

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.

Parameter identification for state estimation: Design of an extended Kalman filter for hybridoma cell fed-batch cultures

The monitoring and optimization of hybridoma cell fed-batch cultures depend on the availability of appropriate on-line sensors for the main culture components. A simple and efficient approach to maintain hybridoma cultures in the optimal operating conditions is to regulate the substrate concentrations at the critical values (G=G<inf>crit</inf> and/or Gn=Gn<inf>crit</inf>) such as to control the hybridoma cells at the critical metabolism state. However, reliable glucose and glutamine probes are currently rare and/or very expensive on the market and it is necessary to design software sensors which are at same time cheap and reliable and that can be used for online measurement. In this study, the overflow metabolism model is used to develop an extended Kalman filter for online estimation of glucose and glutamine in hybridoma cell fed-batch cultures based on the considered available measurements (biomasses (on-line), lactate and ammonia (on-line or off-line)). The observability conditions are examined, and the performances are analysed with simulations of hybridoma cell fed-batch cultures. Glutamine estimation sensitivity is enforced by minimizing a cost function combining a usual least-squares criterion with a state estimation sensitivity criterion.

2013

Metabolic pathway analysis and reduction for mammalian cell cultures-Towards macroscopic modeling

First of all, the aim of this paper is to systematically analyze the metabolism of mammalian cell cultures and reduce the complicated metabolic networks to a manageable macroscopic reaction scheme. Herein, the central carbon metabolism (glycolysis, TCA cycle and glutaminolysis) of glucose and amino acids was investigated whereas the synthetic metabolism of cell and antibody was simply represented with macroscopically balanced reactions. Without losing generality, perfusion and fed-batch cultures of two typical cell lines (hybridoma and GS-CHO) were carried out in bioreactor. With macroscopic balance analysis and metabolic flux analysis (stationary and dynamical), the metabolic networks were rationally reduced thanks to the experimental facts that most of the amino acids (except glutamine, glutamate, and alanine) contributed negligibly to the central carbon metabolism, i.e., they were allocated mainly to the syntheses. Finally, with the aid of analysis of elementary flux mode analysis and extreme pathways, nine macro reactions were derived with physiological definitions.Furthermore, the results from above analyses (MBA, MFA, EFM and EPs) support following conclusions: the respiratory quotient value in mammalian cell culture generally should be near one; several potential metabolic bottlenecks (pyruvate to acetyl-CoA, cytosol NADH translocation into mitochondrion, glutamate dehydrogenation into TCA) may control and regulate cellular metabolism. These results will benefit the future study of dynamic modeling for process monitoring and control. © 2013 Elsevier Ltd.

Hybridoma cell culture optimization using nonlinear model predictive control

This work addresses the application of control systems to the optimization of a monoclonal antibodies (MAb) production chain. The attention is focused on the maximization of hybridoma fed-batch culture productivity. The proposed model presents kinetics showing strong nonlinearities through min-max functions expressing overflow metabolism. A nonlinear model predictive control (NMPC) algorithm, choosing the best trajectory over a moving finite horizon among different sequences of inputs, is suggested in order to optimize productivity. Sensitivities of selected objective functions are considered in a minimax robust version of the NMPC in order to choose the best configuration with respect to practical operating conditions. © IFAC.

Optimal operation of hybridoma cell fed-batch cultures using the overflow metabolism model: Numerical and analytical approach

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 such as to control the hybridoma cells at the critical metabolism state, which allows maximizing the biomass productivity. © IFAC.

Macroscopic modelling of overflow metabolism and model based optimization of hybridoma cell fed-batch cultures

Dynamic modeling of methylotrophic Pichia pastoris culture with exhaust gas analysis: from cellular metabolism to process simulation

2012

Macroscopic modelling of overflow metabolism in fed-batch cultures of hybridoma cells

A macroscopic model that takes into account phenomena of overflow metabolism within glycolysis and glutaminolysis is proposed to simulate hybridoma HB-58 cell cultures. The model of central carbon metabolism is reduced to a set of macroscopic reactions. The macroscopic model describes three metabolism states: respiratory metabolism, overflow metabolism and critical metabolism. It is validated with experimental data of fed-batch hybridoma cultures and successfully predicts the dynamics of cell growth and death, substrate consumption (glutamine and glucose) and metabolites production (lactate and ammonia). Model parameters and confidence intervals are obtained via a non linear least squares identification. This model, on the one hand, allows quantitatively describing overflow metabolism in mammalian cell cultures and, one the other hand, will be valuable for monitoring and control of fed-batch cultures in order to optimize the process.

2010

Linear robust control of S. cerevisiae fed-batch cultures at different scales

In this paper, experimental investigations of an adaptive RST control scheme for the regulation of the ethanol concentration in fed-batch cultures of S. cerevisiae is presented. Our main objective is to prove efficiency and robustness of this controller in experimental applications ranging from laboratory to industrial scales. The controller only requires one on-line measurement signal, making it easily implementable in an industrial environment. Disturbance rejection is ensured thanks to an on-line parameter adaptation procedure, which delivers as a side product an estimate of the growth rate that can be used for process monitoring purposes. The robustification of the controller is achieved in a simple way, using the observer polynomial. © 2009 Elsevier B.V.

Simple metabolic modelling of vero cell growth on glucose in fixed-bed bioreactors

A novel metabolic model is formulated to simulate Vero cell growth on glucose in fixed-bed bioreactors by simplification of glucose fluxes in the central carbon metabolism. Model formulation is based on three designated metabolism states: respiratory metabolism, overflow metabolism and critical metabolism. The model is validated by experimental culture results and successfully predicts the dynamics of cell growth, glucose consumption and lactate production. As well as quantitatively describing glucose overflow metabolism in mammalian cell culture, the proposed model will be helpful for directly monitoring and controlling metabolism state of cells in order to achieve process optimization. © 2010 IFAC.

Monitoring and robust adaptive control of fed-batch cultures of microorganisms exhibiting overflow metabolism

Overflow metabolism characterizes cells strains that are likely to produce inhibiting by-products resulting from an excess of substrate feeding and a saturated respiratory capacity. The critical substrate level separating the two different metabolic pathways is generally not well defined. Monitoring of this kind of cultures, going from model identification to state estimation, is first discussed. Then, a review of control techniques which all aim at maximizing the cell productivity of fed-batch fermentations is presented. Two main adaptive control strategies, one using an estimation of the critical substrate level as set-point and another regulating the by-product concentration, are proposed. Finally, experimental investigations of an adaptive RST control scheme using the observer polynomial for the regulation of the ethanol concentration in Saccharomyces cerevisiae fed-batch cultures ranging from laboratory to industrial scales, are also presented.

2009

Fast and accurate predictions of protein stability changes upon mutations using statistical potentials and neural networks: PoPMuSiC-2.0.

MOTIVATION: The rational design of proteins with modified properties, through amino acid substitutions, is of crucial importance in a large variety of applications. Given the huge number of possible substitutions, every protein engineering project would benefit strongly from the guidance of in silico methods able to predict rapidly, and with reasonable accuracy, the stability changes resulting from all possible mutations in a protein. RESULTS: We exploit newly developed statistical potentials, based on a formalism that highlights the coupling between four protein sequence and structure descriptors, and take into account the amino acid volume variation upon mutation. The stability change is expressed as a linear combination of these energy functions, whose proportionality coefficients vary with the solvent accessibility of the mutated residue and are identified with the help of a neural network. A correlation coefficient of R = 0.63 and a root mean square error of sigma(c) = 1.15 kcal/mol between measured and predicted stability changes are obtained upon cross-validation. These scores reach R = 0.79, and sigma(c) = 0.86 kcal/mol after exclusion of 10% outliers. The predictive power of our method is shown to be significantly higher than that of other programs described in the literature. AVAILABILITY: http://babylone.ulb.ac.be/popmusic

Modeling the temporal evolution of the Drosophila gene expression from DNA microarray time series.

The time evolution of gene expression across the developmental stages of the host organism can be inferred from appropriate DNA microarray time series. Modeling this evolution aims eventually at improving the understanding and prediction of the complex phenomena that are the basis of life. We focus on the embryonic-to-adult development phases of Drosophila melanogaster, and chose to model the expression network with the help of a system of differential equations with constant coefficients, which are nonlinear in the transcript concentrations but linear in their logarithms. To reduce the dimensionality of the problem, genes having similar expression profiles are grouped into 17 clusters. We show that a simple linear model is able to reproduce the experimental data with very good precision, owing to the large number of parameters that represent the connections between the clusters. Remarkably, the parameter reduction allowed elimination of up to 80-85% of these connections while keeping fairly good precision. This result supports the low-connectivity hypothesis of gene expression networks, with about three connections per cluster, without introducing a priori hypotheses. The core of the network shows a few gene clusters with negative self-regulation, and some highly connected clusters involving proteins with crucial functions.

A robust method for the joint estimation of yield coefficients and kinetic parameters in bioprocess models.

Bioprocess model structures that require nonlinear parameter estimation, thus initialization values, are often subject to poor identification performances because of the uncertainty on those initialization values. Under some conditions on the model structure, it is possible to partially circumvent this problem by an appropriate decoupling of the linear part of the model from the nonlinear part of it. This article provides a procedure to be followed when these structural conditions are not satisfied. An original method for decoupling two sets of parameters, namely, kinetic parameters from maximum growth, production, decay rates, and yield coefficients, is presented. It exhibits the advantage of requiring only initialization of the first subset of parameters. In comparison with a classical nonlinear estimation procedure, in which all the parameters are freed, results show enhanced robustness of model identification with regard to parameter initialization errors. This is illustrated by means of three simulation case studies: a fed-batch Human Embryo Kidney cell cultivation process using a macroscopic reaction scheme description, a process of cyclodextrin-glucanotransferase production by Bacillus circulans, and a process of simultaneous starch saccharification and glucose fermentation to lactic acid by Lactobacillus delbrückii, both based on a Luedeking-Piret model structure. Additionally, perspectives of the presented procedure in the context of systematic bioprocess modeling are promising.

2008

Modeling slow-wave activity dynamics: does an exponentially dampened periodic function really fit a single night of normal human sleep?

OBJECTIVE: Slow-wave activity (SWA) is believed to be a fundamental measure of sleep homeostasis and is frequently characterized as an exponentially declining periodic dynamical system. The objective of this study is to carry out the first rigorous statistical test of this hypothesized dynamical behavior. METHODS: Delta power (DP) was computed for each epoch and artifacts were visually scored for 18 randomly selected nights from 18 healthy young men. Non-linear least-squares (LS) combined with the simplex algorithm were used to fit a 7-parameter confirmatory model of DP separately for each individual night of data. Individual night testing was employed because the model must apply to individual night data to be of research or clinical utility. RESULTS: Visually, results appeared satisfactory in half of the cases, though the model was never statistically verified. Validation using simulated data suggested that if the exponentially declining sinusoidal model were correct, satisfactory model fit would be expected on 17/18 nights. CONCLUSIONS: An exponentially dampened periodic function does not fit a single night of sleep amongst healthy young men. Historically, averaging across nights was the primary method used to develop such hypothesized model in order to reduce variability in the data. Our validation with simulated data established that this model does not fit individual night data because the data in an individual night do not conform to an exponentially dampened periodic function and not because of variability. SIGNIFICANCE: Further exploratory work is needed to determine how to optimally model single night SWA data.

State observer scheme for joint kinetic parameter and state estimation

The development and acceptance of model-based monitoring tools in the bioprocess industry is made difficult by the usually large uncertainty associated with the process model. A natural approach to handle this issue is the design of adaptive state observers for the joint estimation of the process state and some of the uncertain model parameters. However, the state extension is often restricted to a few parameters only, for which observability conditions are satisfied with the available measurement information. In this study, this latter issue is circumvented by the combination of two observers: (a) a receding-horizon observer is designed for the joint estimation of the state and uncertain model parameters, and (b) an asymptotic observer, which provides state estimates independently of the kinetic model, is used to provide the missing additional information to the receding-observer, thus avoiding observability loss. This paper derives the properties of this combined state estimation scheme and demonstrates its performance with a realistic simulation case study of animal cell cultures. © 2007 Elsevier Ltd. All rights reserved.

Validation of an automatic comet assay analysis system integrating the curve fitting of combined comet intensity profiles

2007

Systematic decoupled identification of pseudo-stoichiometry, degradation rates and kinetics

Macroscopic models of bioprocesses are very useful to build engineering tools like simulators, software sensors or controllers. These models consist of a system of mass balances for macroscopic species involved in a reaction scheme, which can be determined analytically using a systematic procedure described in Hulhoven, Vande Wouwer, and Bogaerts (2005). Specifically, this procedure generates and compares all the C-identifiable schemes given a set of components for which concentration measurements are available. However, in such macroscopic models, component degradations (e.g. cell lysis) are often neglected, even though they can play a significant role. This paper proposes an extension of the above mentioned procedure which is aimed at the simultaneous estimation of a reaction scheme and component degradation rates. This extended procedure is applied to an industrial enzyme production within fed-batch bacterial cultures. © 2006 Elsevier Ltd. All rights reserved.

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.

Receding-horizon estimation and control of ball mill circuits

This paper focuses on the design of a nonlinear model predictive control (NMPC) scheme for a cement grinding circuit, i.e., a ball mill in closed loop with an air classifier. The multivariable controller uses two mass fractions as controlled variables, and the input flow rate and the classifier selectivity as manipulated variables. As the particle size distribution inside the mill is not directly measurable, a receding-horizon observer is designed, using measurements at the mill exit only. The performance of the control scheme in the face of measurement errors and plant-model mismatches is investigated in simulation. © 2007 Springer-Verlag Berlin Heidelberg.

A general kinetic model structure simulation and experimental validation

In this study, a general kinetic model structure is proposed, which can describe various effects such as activation, inhibition and saturation. Its main advantage lies in an associated identification procedure allowing identifiability problems to be (at least partly) alleviated. The usefulness of the proposed model is tested with simulated as well as with experimental data.

Experimental study of neural network software sensors in yeast and bacteria fed-batch processes

Nowadays, on-line bioprocess monitoring is still a delicate task due to the lack of on-line measurements of the key components of a culture. In this study the use of artificial neural networks (NNs) as a basis to develop software sensors is investigated. Particularly attention is focused on the use of standard signals, such as those coming from pH or oxygen regulation, to infer information on the evolution of biomass or products of yeast and bacteria fed-batch cultures. The selection of informative signals is achieved through principal component analysis (PCA). Radial basis function (RBF) NNs are then used to estimate the component concentrations of interest. This work is based on extensive experimental studies, considering different cell strains and bioreactor scales. The results of our tests demonstrate the flexibility of NN software sensors in industrial environments.

Parameter identification to enforce practical observability of nonlinear systems

The sensitivity of measurements to unmeasured state variables strongly affects the rate of convergence of a state estimator. To overcome potential observability problems, the approach has been to identify the model parameters so as to reach a compromise between model accuracy and system observability. An objective function that weighs the relative importance of these two objectives has been proposed in the literature. However, this scheme relies on an extensive heuristic search to select the weighting coefficients. This paper proposes an objective function that is the product of measures of these two objectives, thus alleviating the need for the trial-and-error selection of the weighting coefficient. The proposed identification procedure is evaluated using both simulated and experimental data, and with different observer structures.

2006

Hybrid extended Luenberger-asymptotic observer for bioprocess state estimation

State observers generate estimates of non-measured variables based on a mathematical model of the process and some available hardware sensor signals. On the one hand, exponential observers, such as Luenberger observers or Kalman filters, have an adjustable rate of convergence, but strongly rely on the accuracy of the process model. On the other hand, asymptotic observers use a state transformation in order to avoid using the (usually uncertain) kinetic model, but have a rate of convergence imposed by the process dilution rate. In an attempt to combine the advantages of both techniques, a hybrid observer is developed, which evaluates a level of confidence in the process model and, accordingly, evolves between the two above-mentioned limit cases (exponential or asymptotic observer). In particular, attention is focused on a hybrid "Luenberger-asymptotic" observer, for which a rigorous stability/convergence analysis is provided. The efficiency and usefulness of the proposed observer is demonstrated with a bioprocess application example. © 2006.

A short note on SPSA techniques and their use in nonlinear bioprocess identification

Transient analysis of a wastewater treatment biofilter - Distributed parameter modelling and state estimation

Mathematical modelling and control of chemical and bio-chemical processes

Monitoring and control of a bioprocess for malaria vaccine production

Based on genetic manipulations, new strains of S. cerevisae are developed, which can be used for the production of pharmaceuticals. In this study, attention is focused on yeast fed-batch cultures dedicated to the production of a malaria vaccine. The efficient operation of this bioprocess requires on-line monitoring and regulation of the ethanol concentration at a low level (so as to maximize biomass productivity). This paper reports on the development of software sensors for the on-line reconstruction of biomass and ethanol, which are based on simple feedforward neural networks making only use of conventional bioprocess instrumentation (stirrer speed, base addition for pH regulation, etc.). This paper also discusses the design of a robust RST control strategy for regulating the ethanol concentration, which ensures setpoint tracking and asymptotic disturbance rejection. Robustification is achieved through the use of Youla parametrisation and on-line adaptation. This control strategy only requires the a priori knowledge about one yield coefficient and one on-line measurement sensor (i.e. an ethanol probe or the proposed software sensor). The software sensor and controller are tested successfully in real-case experimental runs.

2005

On a systematic procedure for the predetermination of macroscopic reaction schemes

Special issue on bioprocess modelling and control

Dynamic modeling of complex biological systems: A link between metabolic and macroscopic description

In this study, a class of dynamic models based on metabolic reaction pathways is analyzed, showing that systems with complex intracellular reaction networks can be represented by macroscopic reactions relating extracellular components only. Based on rigorous assumptions, the model reduction procedure is systematic and allows an equivalent 'input-output' representation of the system to be derived. The procedure is illustrated with a few examples. © 2004 Elsevier Inc. All rights reserved.

Hybrid neural network models of bioprocesses: A comparative study

Modeling of bioprocesses for engineering applications is a very difficult and time consuming task, due to their complex nonlinear dynamic behaviour. in the last years several propositions for hybrid models were published and discussed, in order to combine analytical prior knowledge with the learning capabilities of neural networks. This paper proposes a comparison between several hybrid models based on the two most widespread neural networks, the MultiLayer Perceptron and the Radial Basis Function network. This evaluation relies on simulations of fed-batch bacterial cultures. Copyright © 2005 IFAC.

Maximum likelihood adaptive observer for bioprocesses

A particularity of cell culture processes is the relatively restricted number of valuable and accurate measurements for process control. Software sensors are an interesting solution in response to this problem since it provides non measured state estimation combining the available measurements to a mathematical model. But, due to the complexity of cell culture processes, the mathematical model itself may present some uncertainties particularly in the kinetic description. Such a difficulty has lead to the development of adaptive observers which are designed to jointly estimate state variables and model parameters. However those observers may become particularly di¢ cult to design and to tune as the process complexity increases. in this contribution, an adaptive observer based on the theory of the full horizon and the asymptotic observers is proposed. Copyright © 2005 IFAC.

Systematic procedure for the reduction of complex biological reaction pathways and the generation of macroscopic equivalents

In this study, a class of dynamic models based on metabolic reaction pathways is analyzed, showing that systems with complex intracellular reaction networks can be represented by macroscopic reactions relating extracellular components only. Based on rigorous assumptions, the model reduction procedure is systematic and allows equivalent 'input-output' representations of the system to be derived. The procedure is illustrated with a few examples, and a comparison is made with another recently published method for generating and evaluating macroscopic reaction schemes. © 2004 Elsevier Ltd. All rights reserved.

2004

Biological reaction modeling using radial basis function networks

The difficulty associated with experimental studies of biochemical systems often makes the development of pure black-box neural network models particularly delicate. Hence, it is appealing to resort to a hybrid physical-neural network approach, which uses all the available a priori knowledge about the process, and combines a first-principles model with a partial neural network (NN) model describing the phenomena, which are (at least partly) unknown. In this work, this strategy is applied to a real-case experimental study, i.e. batch CHO animal cell cultures. Several alternative model formulations are considered, including serial model structures, in which neural networks are used to describe either the reaction kinetics or the complete reaction rates (globalizing pseudo-stoichiometry and kinetics), or parallel model structures, in which a NN compensates for the prediction errors of a first-principles model. Attention is focused on the procedure used to estimate the unknown NN parameters and initial conditions from experimental data, including a maximum likelihood approach to take account of all the measurement errors, and a weight decay technique to alleviate identifiability problems. The good model agreement is demonstrated with cross-validation tests. © 2004 Elsevier Ltd. All rights reserved.

Curve fitting of combined comet intensity profiles: A new global concept to quantify DNA damage by the comet assay

The comet assay has become a widely used technique to detect a broad spectrum of DNA damage with the particularity of being performed at cell level. Usual stress quantification methods include individual comet visual examination ("visual scoring") and computer-assisted image analysis. However, a certain subjectivity, loss of information or dispersion of data associated with these methods do not always allow to ascertain low-level genotoxicity nor to exactly quantify damage magnitude. This paper validates on two cell lines (murine lymphoma P388D1 and human melanoma HBL), treated with increasing doses of ethyl methanesulfonate, a new concept developed within the Matlab® environment for DNA damage quantification by comet assay. Instead of collecting data at cell-level, we propose to build a mathematical model from the combination of the sampled comet intensity profiles. The proposed fitting model is the sum of 2 bell-shaped curves. The results show that this mathematical modelling approach represents a good tool to ascertain the presence of DNA damage as well as quantify DNA damage. In this latter case, DNA damage may be quantified either (i) directly from model parameters, or (ii) by recomputing classical morphological comet metrics such as Tail DNA on the fitted profile. © 2004 Elsevier B.V. All rights reserved.

Parameter identification for state estimation - Application to bioprocess software sensors

Together with some on-line measurements, a reliable process model is the key ingredient of a successful state observer design. In common practice, the model parameters are inferred from experimental data so as to minimize a model prediction error, e.g. so as to minimize an output least-squares criterion. In this procedure, no care is actually exercised to ensure that the unmeasured model states are sensitive to the measured states. In turn, if sensitivity is too low, the resulting state observer will probably generate poor estimates of the unmeasured states. To alleviate these problems, a new parameter identification procedure is proposed in this study, which is based on a cost function combining a conventional prediction error criterion with a state estimation sensitivity measure. Minimization of this combined cost function produces a model dedicated to state estimation purposes. A thorough analysis of the procedure is presented in the context of bioreactor modeling, including parameter identification, model validation and design of extended Kalman filters and full horizon observers. © 2004 Elsevier Ltd. All rights reserved.

Fouling resistance modelling, identification and monitoring in a thermosiphon reboiler

Software sensor design for cement grinding circuits-practical issues

Due to the lack of reliable and/or inexpensive hardware sensors in cement grinding, development of software sensors is particularly significant for control and monitoring purposes, In this study, a nonlinear distributed-parameter, full-horizon observer is designed, which allows the contents of the mill to be described in terms of hold-up and particle size distribution. When measurements are available at relatively high sampling rates and at, at least, two spatial locations along the mill, fast observer convergence is obtained. However, in practical situations where measurements can be collected at the mill outlet only and with a relatively low sampling rate, the observer convergence deteriorates, as the sampling rate decreases, performance becomes similar to an asymptotic (simulation) observer. The robustness of the software sensor can be improved by on-line identification of some time-varying parameters, such as the material grindability. These several concepts are discussed and tested in simulation based on a realistic process model.

Stochastic full horizon-asymptotic hybrid observer applied to a simulated cell culture

In an attempt to combine the advantages of an exponential state observer (i.e. fast convergence with an accurate model) and an asymptotic one (i.e. convergence without any knowledge about the kinetic model), a stochastic hybrid observer, which compares the observations made by the two observers has been developed (Hulhoven et al., 2003). This comparison is made in order to perform a test on the process model quality and to provide a state estimation that evolves, accordingly, between the state estimation provided by the exponential observer and the one from the asymptotic one. In this contribution, the stochastic hybrid observer is established by using a full horizon observer as the exponential observer. The performances of this hybrid observer, are then tested on a simulated fed-batch cell culture.

Stochastic hybrid observer for bioprocess state estimation

State observers provide estimates of non-measured variables based on a mathematical model of the process and some available hardware sensor signals. On the one hand, exponential observers, such as the full horizon observer (FHO) or Kaiman filters, have an adjustable rate of convergence, but strongly rely on the accuracy of the process model. On the other hand, asymptotic observers use a state transformation in order to avoid using the (usually uncertain) kinetic model, but have a rate of convergence imposed by the process dilution rate. In an attempt to combine the advantages of both techniques, a hybrid observer is developed. The principle of this hybrid observer is to compare the observations made by the two observers in order to perform a test on the process model quality and to provide, accordingly, a state estimation that evolves between the two above-mentioned limit observations (observations from an exponential or the asymptotic observer).

Systematic decoupled identification of pseudo-stoichiometry, lysis rate and kinetics for a xylanase production

Macroscopic models of bioprocesses are very useful to build engineering tools like simulators, software sensors, controllers,... This kind of models consists of a system of mass balances for the macroscopic species involved in a reaction scheme. Such a reaction scheme can be determined analytically by a systematic procedure to generate and compare all the C-identifiable schemes given a set of components for which concentration measurements are available. This paper presents the application of this procedure to the modelling of a xylanase production within fed-batch bacterial cultures. Moreover, the adaptation of the procedure to estimate simultaneously the cell lysis rate is described.

State and parameter estimation in cement grinding circuits-practical aspects

Due to the lack of reliable and/or inexpensive hardware sensors in cement grinding, development of software sensors is particularly significant for control and monitoring purposes. In this study, a nonlinear distributed-parameter, full-horizon observer is designed, which allows the contents of the mill to be described in terms of hold-up and particle size distribution. When measurements are available at relatively high sampling rates and at, at least, two spatial locations along the mill, fast observer convergence is obtained. However, in practical situations where measurements can be collected at the mill outlet only and with a relatively low sampling rate, the observer convergence deteriorates and, as the sampling rate decreases, performance becomes similar to an asymptotic (simulation) observer. The robustness of the software sensor can be improved by on-line identification of some time-varying parameters, such as the material grindability. These several concepts are discussed and tested in simulation based on a realistic process model.

Modelling and optimal experiment design for cultures of S. Cerevisiae

In this paper, an unstructured model based on Sonnleitner's model is presented and an identification procedure for five kinetic parameters is developed on the basis of the optimal experimental design theory. When the number of estimated parameters is larger than two, the difficulty associated with the selection of input signals with enough degrees of freedom for an accurate identification of all the parameters is highlighted. It is shown that a simultaneous decomposition of the model and the optimisation problem allows input signals to be selected, which sufficiently excite the bioprocess and allow the required level of decorrelation and accuracy to be achieved.

Systematic model identification of complex bioprocesses: Application to a CHO-K1 cell culture

Modeling and parameter identification are important prerequisites for state estimation and control of complex biological systems in bioengineering. Due to the great variety of cell lines and the rapidity of developments in genetics, biosystems have to be investigated in a fast and efficient way to identify the major metabolic phenomena. This paper proposes a systematic modeling procedure, which enables the description of the most important experimental settings and biological effects in terms of stoichiometry, kinetics and metabolic regulation. This procedure is successfully applied to the real case of a perfused mammalian cell culture of non-transfected CHO-K1 cells in suspension.

2003

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.

Maximum likelihood estimation of pseudo-stoichiometry in macroscopic biological reaction schemes

Identification of pseudo-stoichiometric (or yield) coefficients is of primary importance for building a bioprocess model. In most of the applications, the estimation of these coefficients has to be performed without any knowledge of the kinetics and on the basis of a few experiments for which noisy discrete measurements of component concentrations are available. This paper proposes maximum likelihood estimators which are able to deal with measurement errors on all the signals, at each sampling time (including the initial one) and with intrinsic sign constraints on the parameters. This kind of realistic hypotheses exclude the use of the usual (weighted) least-squares estimators. The maximum likelihood estimators are proved to be unbiased (provided a first-order approximation) and their estimation error covariance matrix can be computed (at the same level of first-order approximation). The solutions are proposed in a very general framework, dealing with cell cultures (of bacteria, yeasts or animal cells) performed in stirred tank (continuous, semi-batch or batch) reactors, and without any a priori knowledge on the kinetics. The use of the estimators and their statistical properties are illustrated in a simulation case study (fed-batch bacterial cultures) and in a real case one (batch animal cell cultures). © 2003 Elsevier Science Ltd. All rights reserved.

From dynamic metabolic modeling to unstructured model identification of complex biosystems

In this study, a class of dynamic models based on metabolic reaction pathways is analyzed, showing that systems with complex intracellular reaction networks can be represented by macroscopic reactions relating extracellular components only. Based on rigorous assumptions, the model reduction procedure is systematic and allows an equivalent 'input-output' representation of the system to be derived. The procedure is illustrated with a few examples.

2002

Hybrid full horizon-asymptotic observer for bioprocesses

The full horizon observer is a stochastic nonlinear observer that does not require any parameter tuning and whose optimal feature results directly from the identification cost function of the initial conditions. The efficiency of this observer is, however, strongly dependent on the model quality. On the other hand, the asymptotic observer does not require a kinetic model. However, its convergence is function of the experimental conditions. The aim of this study is to build a hybrid observer which allows to jointly estimate the state and identify on-line the confidence in the kinetic model. Simulations of fed-batch bacterial cultures show very satisfactory results.

2001

Stability parameter estimation at ambient temperature from studies at elevated temperatures

Neural network applications in non-linear modelling of (bio)chemical processes

In recent years, neural networks have attracted much attention for their potential to address a number of difficult problems in modelling and controlling nonlinear dynamic systems, especially in (bio) chemical engineering. The objective of this paper is to review some of the most widely used approaches to neural-network-based modelling, including plain black box as well as hybrid neural network - first principles modelling. Two specific application examples are used for illustration purposes: a simple tank level-control system is studied in simulation while a challenging bioprocess application is investigated based on experimental data. These applications allow some original concepts and techniques to be introduced.

On-line state estimation of bioprocesses with full horizon observers

“Feedback” and “feedforward” conditioning techniques

It is generally admitted that the classical conditioning technique is restricted to some application conditions like the bi-property of the controller and its inverse stability. Some extensions to overcome these restrictions are recalled in the paper. The conditioning technique has been conceived and must always be considered as an a posteriori anti-windup method (the a priori knowledge of the non-linearity acting on the desired control variable has not to be known, provided a post-measurement of the actual control variable is available). Hence, this kind of "feedback" anti-windup should always be used because it is never possible to prejudge of any non-linearity that could appear. However, when an a priori knowledge of some non-linearities is available, it is possible to include this knowledge either in the synthesis of the controller or in the design of a "feedforward" anti-windup. Two methods of feedforward anti-windup are given in the paper, namely the optimal conditioning and the predictive conditioning techniques. We propose to keep the term conditioning for these last anti-windup schemes, because as in the classical conditioning technique, we try to "condition" the controller to be able to carry on, as soon as possible, in the same way as in the linear case. © 2000 EUCA.

2000

Improved kinetic parameter estimation in pH-profile data treatment

Statistical problems in temperature stability parameter estimation have been the subject of many papers whereas statistics in, pH-profile parameter estimation have focused little attention. However, the conventional two step method used in data treatment in both cases leads to identical statistical problems. The aim of this study is then to introduce a method that improves statistics in pH-profile parameter estimation. A one step non-linear method that takes into account the errors in drug content determination is proposed. A mathematical relationship between drug content C, pH and time t is tested. The proposed method allows the estimation of the specific kinetic constants and the dissociation constant (pK(a)) in a single run. The most likely experimental initial drug contents C(0j),. where j is the index of a given experiment, are also determined. This approach that takes into account all relevant experimental information for the estimation of kinetic parameters is more rigorous from a statistical viewpoint than the classical two step methods. Kinetic data from acetylsalicylic acid (ASA) hydrolysis was used for the tests. (C) 2000 Elsevier Science B.V.

Kinetic modelling and parameter identification for simulation and state estimation of bioprocesses

Modellidentifikation zur zustandsschätzung - Anwendung auf einen bioprozess

Based on a process model and some available measurements, state observers allow unmeasured states to be reconstructed on-line. When the underlying process model is established, the unknown parameters are usually identified by minimizing a least-squares or maximum likelihood criterion, which makes use of off-line measurements of the complete state vector. These conventional criteria do not express the condition that the model of the unmeasured part of the state should be sensitive to the measured one. In this study, a new cost function is proposed, which attempts to enforce a higher model sensitivity by combining a classical maximum likelihood criterion with a scalar measure of the model sensitivity. © Oldenbourg Verlag.

Maximum likelihood parameter estimation of a hybrid neural-classical structure for the simulation of bioprocesses

This paper proposes a hybrid structure for the modeling of a bioprocess: classical (in the form of a priori knowledge describing the mass balances) and neural (a radial basis function network describing the nonlinear reactions kinetics within these mass balances). The aim is to build a continuous simulator capable to reconstruct from initial conditions the trajectory of state variables (i.e. the main component concentrations) by considering also an aspect which usually is not taken into account in bioprocess modeling: the existence of important measurement errors. A clustering strategy is used for placing the Gaussian centers and a maximum likelihood cost function is defined for the estimation of the network weights and initial conditions for the simulator. The structure is tested on batch animal cell cultures for which rare and asynchronous measurements are available: glucose, glutamine, lactate and biomass concentrations. ©2000 IMACS/Elsevier Science B.V. All rights reserved.

1999

Incorporating batch effects in the estimation of drug stability parameters using an Arrhenius model

The nonlinear estimation of drug stability parameters (energy of activation E(a) and shelf-life t(Y)) by conventional approaches employs equations relating drug content determination C at time t and temperature T. The identification procedures lead to the determination of only one initial drug content C0 for several different experiments. However, it is well known that because of experimental concentration variation or of intentional modification of the experimental schedule, there are as many initial drug contents as experiments. For these reasons, a method which takes into account batch effects is proposed to determine stability parameters and also all initial drug contents C(0j) where j is the index of experiment in one step. This method is more accurate from a statistical viewpoint and is suitable for data treatment in pharmaceutical industries where the initial drug content of each batch entering the stability program can be checked a posteriori. The application of this method is shown on real kinetic data from the hydrolysis of acetylsalicylic acid (ASA). Copyright (C) 1999 Elsevier Science B.V.

Multidrug resistance modifies polyamines uptake in P388 murine lymphoma cells: Experimental and modeling approach

Polyamines (putrescine, spermidine and spermine) are ubiquitous compounds, essential for cell growth. This paper compares the polyamine transport between sensitive P388 murine lymphoma cells and two multidrug resistant P388 sublines with the assistance of an experimental model. This new model allows the characterisation of the whole polyamines uptake and efflux. Three parameters are identified by the model: two rate constants (K+ for the uptake and K- for the efflux) which are considered as physical constants specific to the transport of one polyamine in one cell type, and Ci(o) which represents the initial intracellular concentration. This model well describes our experimental results of polyamine transport across the P388 cell plasma membrane. Multidrug resistant P388 cells exhibit spermine uptake significantly higher than that of sensitive cells when on the opposite, putrescine enters more rapidly into the sensitive P388 cells. In conclusion, comparison of polyamine transport between sensitive and multidrug resistant P388 phenotypes shows large and significant differences. Copyright (C) 1999 Elsevier Science B.V. All rights reserved.

A hybrid asymptotic-Kalman observer for bioprocesses

A general mathematical modelling technique for bioprocesses in engineering applications

A new training method for hybrid models of bioprocesses

1998

Identification for fault detection in an industrial condenser

The condenser of a batch distillation column, equipped with temperature and flow sensors, is considered here. The aim of the paper is to build a system that is able to detect flow sensor failures occurring in a batch. Three methods are considered. For all of them, the first step consists of the parameter identification of a grey-box model. For the first two tests, the classical least-squares approach is used. The first fault-detection test is based on the value of the sum of the squares of the prediction errors obtained with the current batch measurements. The second one is a classical hypothesis test, relying on the log-likelihood ratio. Both methods are shown to lack robustness with respect to the process variability from batch to batch. A third approach is then investigated, in which the optimised cost function of the identification phase is chosen in order to reflect the sensitivity of the model to the flow sensor faults. It yields significantly better results than the other two methods for the data being considered. © 1998 Elsevier Science Ltd. All rights reserved.

1996

Analytical solution of the non uniform heat exchange in a reactor cooling coil with constant fluid flow

An analytical solution of the partial differential equation describing the enthalpy balance of the cooling fluid in a batch exothermic reactor has been developed for a constant flow. Thanks to an analytical integration on position, the simulation of the process can be performed with one independant variable (time) and without any approximation on the profile of the cooling fluid temperature. Comparisons are made with the well-known approximate method of segmentation into finite volumes at uniform temperature. The proposed method requires the integration of one ordinary differential equation (ODE) instead of the system of N + 1 ODEs used in the N finite volumes method. It is shown in simulations that a small number of finite elements (one to six) leads to a large inaccuracy in the results, however, it is commonly used. Finally the analytic method is applied as a zeroth order approximation to the case of a time varying flow. Comparisons are also made with the finite elements method and shown very good simulation results.

1994

Mathematical modelling and control of a chemical batch reactor