Design of on-line state estimators for a recombinant E. coli fed-batch fermentation

In recent years a remarkable effort has been made in the development of new sensors and process analytical technology. However, it is still difficult to find reliable and low cost commercial sensors for on-line measurements of important variables. Therefore, considerable attention has been focused on the development of on-line software sensors. Nevertheless, the application of those algorithms to complex biological processes is still very incipient. In this work two different state estimators have been studied regarding their applicability to the recombinant Escherichia coli fed-batch fermentation. Both algorithms showed the ability to estimate on-line biomass and acetate concentrations. However, the extended Kalman observer exhibited a better convergence in spite of being less flexible regarding the combination of the measured and estimated variables.PRODEP ; Fundação para a Ciência e a Tecnologia (FCT

Identification of yield coefficients in an E. coli model : an optimal experimental design using genetic algorithms

An optimal experimental design for yield coefficients estimation in an unstructured growth model of fed-batch fermentation of E. coli is presented. The feed profile is designed by optimisation of a scalar function based on the Fischer Information Matrix. A genetic algorithm is proposed as the optimisation method due to its efficiency and independence on the initial values.Programa de Desenvolvimento Educativo para Portugal (PRODEP).Fundação para a Ciência e a Tecnologia (FCT) – PRAXISXXI/BD/16961/98

On-line estimation of biomass in an E. coli fed-batch fermentation

In this work, an Extended Kalman Observer is applied to the on-line determination of biomass concentration in a high-cell density fed-batch fermentation of Escherichia coli. Although the importance of this fermentation process for the biopharmaceutical industry is widely recognized, there are still several difficulties associated with the design of monitoring and control algorithms that could improve the performance of the process by decreasing the production costs and increasing the yield. In this process, biomass concentration has an important role for model predictive control, estimation of specific growth rates, prevention of acetate accumulation and optimization of the production of recombinant proteins (regarding both productivity and moment of induction). However, nowadays it is still determined using off-line laboratory analysis, making it of limited use for control purposes. For the development of the Extended Kalman Observer, a dynamical mathematical model of the process was used, which includes balance equations for the main state variables (biomass, glucose, acetate, dissolved oxygen and carbon dioxide concentrations) together with a complex kinetic model describing the 3 main metabolic pathways of Escherichia coli. The observer applied in this work requires the on-line measurement of a subset of state variables (dissolved oxygen and carbon dioxide concentrations) together with broth weight and gaseous mass transfer rates. State-of-the-art sensors were used for measuring dissolved oxygen and carbon dioxide concentrations and gaseous transfer rates were determined on-line using commercial gas analysers. The calculations were performed on-line in a developed LabVIEW data acquisition and control system. The extended Kalman observer exhibited a good convergence to the real values of biomass concentration, with a very low quadratic difference between experimental and estimated data. Also, the sampling frequency for the measured variables is compatible with the existing experimental data.Programa de Desenvolvimento Educativo para Portugal (PRODEP)

Design of interval observers for an E. coli fed-batch fermentation with uncertain inputs

In bioreactors, the measurement of variables that play a key role in the quality and productivity of fermentations, is of major importance. However, their direct measurement is often expensive or even impossible considering the current sensor technology. Therefore, on-line estimation of unmeasured variables in bioreactors can be an interesting approach. The objective of this work is to introduce an alternative solution for the state observation of bioprocesses in cases where the kinetic model is unclear and the concentration of the influent substrates is badly known, a situation that is common in many practical applications. The high-cell density fed-batch fermentation of Escherichia coli is studied in terms of applicability of a simple interval observer for the estimation of relevant variables of the process, when uncertainties of the process inputs exist. The simple interval observer is designed on the basis of the cooperativity properties of the observer error dynamics (Rapaport and Dochain, 2005). Further assumptions are the knowledge of the (lower and upper) bounds of the influent substrate concentration. Furthermore, an appropriate state transformation and conditions that guarantee system cooperativity have been introduced for that purpose. The performance of the interval observer is illustrated through numerical simulation.Programa de Desenvolvimento Educativo para Portugal (PRODEP)

Estimation of biomass concentration using interval observers in an E. coli fed-batch fermentation

In bioreactors, the measurement of variables that play a key role in the quality and productivity of fermentations, is of major importance. However, their direct measurement is often expensive or even impossible considering the current sensor technology. Therefore, on-line estimation of unmeasured variables in bioreactors can be an interesting approach. The objective of this work is to introduce an alternative solution for the observation of biomass concentration in E. coli fed-batch fermentations, in cases where the kinetic model is unclear and several variables, like the concentration of the influent substrates and the initial values of the state variables are badly known, a situation that is common in many practical applications. The simple interval observer is designed on the basis of the cooperativity properties of the observer error dynamics (Rapaport and Dochain, 2005). The performance of the interval observer is illustrated through numerical simulation and it was found that the observer deal well with uncertainties up to 50% and with white noise in the variables measured on-line. The interval obtained for the biomass estimation is also quite narrow, indicating that it is possible to accurately predict biomass concentration under the presence of uncertainties.Programa de Desenvolvimento Educativo para Portugal (PRODEP)Fundação para a Ciência e a Tecnologia (FCT) - Projecto recSysBio POCI/BIO/60139/200

Monitoring of fed-batch E. coli fermentations with software sensors

Accurate monitoring and control of industrial bioprocess requires the knowledge of a great number of variables, being some of them not measurable with standard devices. To overcome this difficulty, software sensors can be used for on-line estimation of those variables and, therefore, its development is of paramount importance. An Asymptotic Observer was used for monitoring Escherichia coli fed-batch fermentations. Its performance was evaluated using simulated and experimental data. The results obtained showed that the observer was able to predict the biomass concentration profiles showing, however, less satisfactory results regarding the estimation of glucose and acetate concentrations. In comparison with the results obtained with an Extended Kalman Observer, the performance of the Asymptotic Observer in the fermentation monitoring was slightly better.recSysBioPrograma de Desenvolvimento Educativo para Portugal III (PRODEP

Optimização de estratégias de alimentação para identificação de parâmetros de um modelo de E. coli. utilização do modelo em monitorização e controlo

Doutoramento em Engenharia Química e BiológicaOs principais objectivos desta tese são: o desenho óptimo de experiências para a identificação de coeficientes de rendimento de um modelo não estruturado de um processo de fermentação semicontínua de Escherichia coli; a verificação experimental das trajectórias de alimentação obtidas por simulação; o desenvolvimento de estratégias de monitorização avançada para a estimação em linha de variáveis de estado e parâmetros cinéticos; e por fim o desenvolvimento de uma lei de controlo adaptativo para controlar a taxa específica de crescimento, com base em estratégias de alimentação de substrato com vista à maximização do crescimento e/ou produção. São apresentadas metodologias para o desenho óptimo de experiências, que visam a optimização da riqueza informativa das mesmas, quantificada por índices relativos à Matriz de Informação de Fisher. Embora, o modelo utilizado para descrever a fermentação semi-contínua de E. coli não esteja ainda optimizado em termos cinéticos e de algumas dificuldades encontradas na implementação prática dos resultados obtidos por simulação para o desenho óptimo de experiências, a qualidade da estimativa dos parâmetros, especialmente os do regime respirativo, é promissora. A incerteza das estimativas foi avaliada através de índices relacionados com o modelo de regressão linear múltipla, índices relativos à matriz de Fisher e pelo desenho das correspondentes elipses dos desvios. Os desvios associados a cada coeficiente mostram que ainda não foram encontrados os melhores valores. Procedeu-se também à investigação do papel do modelo dinâmico geral no desenho de sensores por programação. Foram aplicados três observadores – observador estendido de Kalman, observador assimptótico e observador por intervalo – para estimar a concentração de biomassa, tendo sido avaliado e comparado o seu desempenho bem como a sua flexibilidade. Os observadores estudados mostraram-se robustos, apresentando comportamentos complementares. Os observadores assimptóticos apresentam, em geral, um melhor desempenho que os observadores estendidos de Kalman. Os observadores por intervalo apresentam vantagens em termos de implementação prática, apresentando-se bastante promissores embora a sua validação experimental seja necessária. É apresentada uma lei de controlo adaptativo com modelo de referência que se traduz num controlo por antecipação/retroacção cuja acção de retroacção é do tipo PI, para controlar a taxa específica de crescimento. A robustez do algoritmo de controlo foi estudada por simulação numérica gerando dados “pseudo reais”, por aplicação de um ruído branco às variáveis medidas em linha, por alteração do valor de referência, por alteração do valor da concentração da glucose na alimentação e variando os valores nominais dos parâmetros do modelo. O estudo realizado permite concluir que a resposta do controlador é em geral satisfatória, sendo capaz de manter o valor da taxa específica de crescimento na vizinhança do valor de referência pretendido e inferior a um valor que conduz à formação de acetato, revestindo-se este facto de grande importância numa situação real, em especial, numa fermentação cujo objectivo seja a produção, nomeadamente de proteínas recombinadas. Foram ainda, analisados diferentes métodos de sintonização dos parâmetros do controlador, podendo concluir-se que, em geral, o método de sintonização automática com recurso à regra de adaptação dos parâmetros em função do erro relativo do controlador foi o que apresentou um melhor desempenho global. Este mecanismo de sintonização automática demonstrou capacidade para melhorar o desempenho do controlador ajustando continuamente os seus parâmetros.The main objectives of this thesis are: the optimal experiment design for yield coefficients estimation in an unstructured growth model for Escherichia coli fed-batch fermentation; the experimental validation of the simulated feed trajectories; the development of advanced monitoring strategies for the on-line estimation of state variables and kinetic parameters; and at last the development of an adaptive control law, based on optimal substrate feed strategies in order to increase the growth and/or the production. Methodologies for the optimal experimental design are presented, in order to optimise the richness of data coming out from experiments, quantified by indexes based on the Fisher Information Matrix. Although the model used to describe the E. coli fed-batch fermentation is not optimised from the kinetic properties point of view and the fact that some difficulties were encountered in practical implementation of the simulated results obtained with the optimal experimental design, the estimated parameter quality, especially for the oxidative regimen, is promising. The estimation uncertainty was evaluated by means of indexes related with multiple linear regression model, indexes related to the Fisher matrix as well as by the construction of the related deviation ellipses. The deviations associated to each coefficient show that the best values were not yet found. The role of the general dynamical model was also investigated in which concerns the design of state observers, also called software sensors. The performance of three observer classes was compared: Kalman extended observer, assimptotic observer and interval observer. The studied observers showed good performance and robustness, being complementary of each other. Assimptotic observers showed, in general, a better performance than the Kalman extended observer. Interval observers presented advantages concerning practical implementation, showing a promising behaviour although experimental validation is needed. A model reference adaptive control law is presented and can be interpreted as a PI like feedforward/feedback controller, for specific growth rate control. Algorithm robustness was studied using “pseudo real” data obtained by numerical simulation, by applying a white noise to the on-line measured variables, by modifying the set-point value, by changing the glucose concentration value of the feed rate and varying the nominal model parameter value. The study made allowed to conclude that the controller response is, generally, satisfactory being able to keep the specific growth rate value in the proximity of the desired set-point and lower than the value that permits acetate formation, which is of major importance namely for real cases, specially, in a fermentation which objective was the production of recombinant proteins. Different tuning devices for controller parameters were analysed being the better performance achieved by the automatic tuning method with an adaptation rate as a function of the controller relative error. This automatic tuning mechanism was able to improve the controller performance adjusting continuously its parameters

Evolutionary algorithms for offline and online optimization of fed-batch fermentation processes

In this work, Evolutionary Algorithms (EAs) were used to control a recombinant bacterial fed-batch fermentation process that aims to produce a biopharmaceutical product. Initially, a novel EA, based on real-valued representations and that makes use of individuals with variable sized chromosomes, was used to optimize the process, prior to its run (offline optimization), by simultaneously adjusting the feeding trajectory, the duration of the fermentation and the initial conditions of the process2. A white box mathematical model derived from literature1 and fine tuned by practice was used in the fitness function, based on differential equations and kinetic algebraic equations. Outstanding productivity levels were obtained and the results are validated by practice. Finally, online optimization is proposed, where the EA is running simultaneously with the fermentation process, receiving information regarding the process, updating its internal model and reaching new solutions that will be used to online control. Results obtained by simulation of the system show that without online optimization minor changes cause the process to reach sub-optimal levels in the long run. On the other hand, when online optimization is performed, minor changes are corrected and the behaviour of the system is near optimal

Application of genome-scale metabolic models to the optimization of recombinant protein production in Escherichia coli

Escherichia coli has been the organism of choice for the production of many recombinant proteins with high therapeutic value. However, while the research on molecular biology has allowed the development of very strong promoters, there are still some phenomena associated with this process that hamper the full use of those technologies: aerobic acetate production associated with high specific growth rates, and the so-called stringent response that usually occurs when very high levels of heterologous protein production takes place. In both cases, productivity is affected due to a decrease in the specific growth and production rates. In this work, a systems biology approach for modelling recombinant protein production processes was used aiming its optimization. The existing genome-scale metabolic model of Escherichia coli was modified by including an equation for protein production (the model protein GFP – Green Florescent Protein), based on its amino acids content. For the validation of the genome-scale model in high-cell density processes, highly reproducible fed-batch fermentations are run with constant specific growth rate. The developed data acquisition and control system allows to control the substrate addition rate, and to acquire on-line the fermenter’s weight, to calculate oxygen and carbon dioxide transfer rates, as well as to obtain glucose and acetate concentrations using a developed Flow Injection Analysis system