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A simple observer-based feedback strategy for controlling fed-batch hybridoma cultures Federico Alberto Gorrini, Silvina Ines Biagiola, Jose Luis Figueroa, and Alain Wouwer Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b03395 • Publication Date (Web): 02 Dec 2017 Downloaded from http://pubs.acs.org on December 3, 2017
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Industrial & Engineering Chemistry Research
A Simple Observer-Based Feedback Strategy for Controlling Fed-Batch Hybridoma Cultures Federico A. Gorrini†, Silvina I. Biagiola†, José L. Figueroa†*, and Alain Vande Wouwer‡ † Instituto de Investigaciones en Ingeniería Eléctrica “Alfredo Desages,” UNS-CONICET. San Andrés 800, Palihue, 8000 - Bahía Blanca, ARGENTINA. ‡ Laboratoire d'Automatique, Faculté Polytechnique de Mons, 31 Boulevard Dolez, 7000 Mons, BELGIUM *
[email protected] KEYWORDS: process control, state estimation, input observer, optimizing control, bioprocess.
ABSTRACT - Cultures of hybridoma cells in bioreactors are commonly used to produce monoclonal antibodies. As an alternative to nonlinear model predictive control, which has recently been applied successfully to optimize the process productivity, a simpler control approach is developed in the present study. This strategy is based on a classical PI controller and software sensors for the reaction rates, which exploit the particular structure of the dynamic model. The dynamic behavior of the process can indeed be subdivided into four operating zones, depending on the overflow metabolism of the hybridoma cells. In addition, robustness towards model uncertainties and measurement noise is investigated.
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1. INTRODUCTION Hybridoma cells are hybrid cells resulting from the fusion of a lymphocyte and a tumor cell. The interest in cultivating hybridoma cells lies in their capacity to produce specific monoclonal antibodies. For this reason, the pharmaceutical industry pays attention to the development of adequate bioprocesses, including the formulation of culture media, and more recently, on the feeding policy and possibly some form of automatic control strategy in order to improve performance and productivity. In an attempt to describe the evolution of the cultures, different kinetic models were developed. One of the most recent and appropriate for process control is the dynamic model proposed by Amribt et al.1. Cellular metabolism can follow two routes according to the available substrate concentration: the respiratory mode (below a threshold substrate) or the respiro-fermentative mode (with excess substrate) that generates inhibitory products (lactate and ammonia). From a control point of view, the objective is to select an operation mode that maximizes the production of antibodies (or equivalently the production of biomass). To reach the optimum while avoiding the inhibitory regime, Dewasme et al.2 resort to a closed loop optimization. Several optimizing control strategies dedicated to bioprocesses have been reported in the literature, including adaptive control, probing, robust and predictive control3-6. The use of nonlinear predictive control (NMPC)7 provides a natural and well-accepted structure for the formulation of optimal feedback control under constraints. A simple and efficient approach to maintain the hybridoma culture in the optimum operation condition is the regulation of glucose and glutamine concentrations at their critical levels5,8-9.
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Industrial & Engineering Chemistry Research
However, the sensors currently available for these types of measurements are expensive and delicate to use (in terms of acquisition, maintenance and operational costs). For this reason, observers are frequently included in the control structure. Dewasme et al.7 proposed a predictive controller based on the minimization of the deviation of the concentrations of glutamine and glucose from their critical values, thus maintaining the culture at the limit of the overflow metabolism. For control implementation in the industry, the simplicity of the control strategy remains however an important constraint. Therefore, the objective of this study is to explore the possibility of designing a simple, yet robust, PID-like controller, based on the on-line estimation of the reaction rates. An original contribution is the development of a state estimation scheme which exploits the particular structure of the dynamic model. Moreover, the presence of parametric uncertainty is addressed. This paper is organized as follows. In Section 2, the mathematical model of hybridoma HB-581 is briefly described, whereas Section 3 is dedicated to control design. NMPC is first presented, as it will serve as a basis for comparison, and then attention is focused on the development of simple PI controllers for the reaction rates. Moreover, the design of an observer tailored to the application is detailed, based on a minimum variance unknown input observer10. The performance achieved with the proposed feedback controller is compared to the results obtained using NMPC7. Conclusions and perspectives end this paper in Section 4.
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2. PROCESS MODEL Hybridoma culture involves viable biomass (Xv) growth based on glucose and glutamine (G and Gn, respectively) consumption. A macroscopic model1 based on the reduced metabolic network of HB-58 is the following: φG
Glucose consumption: G → aX + bL
(1a)
φGn
Glutamine consumption: Gn → cX + dN
(1b)
φOver −G
Glucose overflow: G → 2 L φOver −Gn
Glutamine overflow: Gn → N +
(1c)
1 L 2
(1d)
where L and N represent lactate and ammonia, respectively. The symbols a, b, c and d are the stoichiometric coefficients and ϕi (i=G, Gn, Over-G, Over-Gn) are the reaction rates given by the discontinuous overflow kinetic model recalling the bottleneck assumption11 of: ϕ G = min( ϕ G1 , ϕ Gmax )
(2a)
ϕ Gn = min( ϕ Gn1 , ϕ Gnmax )
(2b)
ϕ Over −G = max( 0, ϕ G1 − ϕ Gmax )
(2c)
ϕ Over −Gn = max( 0, ϕ Gn1 − ϕ Gnmax )
(2d)
Each rate is the product of Monod-type specific consumption rates Γi (i = G1, Gn1, Gmax, Gnmax) and the concentration of viable biomass Xv as in:
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ϕ G1 = ΓG1 X v = µGmax1
G Gn Xv K G + G K Gn1 + Gn
ϕ Gn1 = ΓGn1 X v = µGnmax1
Gn KN Xv K Gn + Gn K N + N
(3a)
(3b)
ϕ Gma x = ΓGma x X v = µ Gm ax 2 X v
(3c)
ϕ Gnma x = ΓGnma x X v = µ Gnm ax 2 X v
(3d)
where µimaxj (i=G,Gn; j=1,2) are the maximum values of the specific kinetic rates and KG, KGn1 and KGn are the half-saturation coefficients. KN is the ammonia inhibition constant over the oxidation of glutamine. This representation is based on the kinetic model contributed by Sonnleitner and Käppeli11 which rests on the hypothesis that the strain metabolism is regulated by its respiratory capacity. When substrate is in excess (for instance, when glucose concentration is above the critical level G>Gcrit and the consumption rate is ΓG1>ΓGmax), the cells produce lactate following the fermentative path and, therefore, the culture is in respiro-fermentative mode. On the other hand, when substrate becomes limiting (for instance, glucose concentration is below a critical level G
