Optimal dynamic experiments for bioreactor model discrimination

 This paper describes a general approach fordynamic model discrimination for continuous cultures and presents dynamic models for pure cultures of E. coli and C. utilis obtained using the method. For each pure culture system, four candidate models representing various levels of structure were considered. All models reduce to Monod growth kinetics at steady state. An optimized set of multivariable step inputs in selected manipulative variables was used to discriminate between candidate models. The models that best predicted the dynamic behavior were selected by comparison of model predictions with experimental data. Two discrimination functions were compared in terms of their ability to determine the optimal set of multivariable step inputs to discriminate between candidate models. Results indicate that model discrimination based on maximizing the minimum absolute difference between any two models for a given set of inputs possessed good potential for discrimination between candidate models. Models selected for E. coli andC. utilis from the model discrimination work arepresented and compared with experimental data. Received: 24 May 1994/Received revision: 28 September 1994/Accepted: 5 December 1994     

Multilayer adaptive control of continuous bioprocesses using optimising control technique. Case study: Bakers' yeast culture

High costs associated with many fermentation processes in an increasingly competitive industry make any prompt application of modern control techniques to industrial bioprocesses very desirable. However, this is often hampered by the lack of adequate mathematical models, on the one hand, and by the absence of continuous, on-line measurement of the most relevant process variables, on the other hand. This paper addresses these problems and offers a new strategy to control continuous bioprocesses using a hierarchical structure such that neither structured process models nor continuous measurement of all relevant variables have to be available. The control system consists of two layers. The lower layer represents a dynamic adaptive follow-up control of a continuously measured output — in our case dissolved oxygen concentration. This variable is supposed to be strongly correlated with the key output variable — in our case cellular concentration which is not continuously available for measurement. The higher layer is then designed to maintain a desired profile of the process key output using a set-point optimising control technique. The Integrated System Optimisation and Parameter Estimation method used operates on an appropriately chosen steady-state performance criterion. A prerequisite for successful application of the proposed approach is an approximate steady-state model, describing the relationship between the measured output and the process key output variable. Furthermore, occasional in situ, off-line or laboratory measurement values of the key output variable are needed. Promising simulation results of the biomass concentration control, by manipulating the air flow-rate in the continuous bakers' yeast culture are presented.     

Overexpression of cloned genes using recombinant Escherichia coli regulated by a T7 promoter: II. Two-stage continuous cultures and model simulations

A two-stage culture strategy was studied for continuous high-level production of a foreign protein in the chemically inducible T7 expression system. The first stage is dedicated to the maintenance of plasmid-bearing cells and the second stage to the target protein synthesis by induction of cells coming from the first stage. On entering the second stage, recombinant cells undergo a gradual induction of the target gene expression. These plasmid-bearing cells experience dynamic changes in intracellular compositions and specific growth rates with their individual residence times. Therefore, the overall cultural characteristics in the production stage are really averages of the contributions from the various cells with different residence times. The behavior of the two-stage culture is described by a model, which accounts for dynamic variations of cell growth and protein synthesis rates with cell residence times. Model simulations were compared with experimental results at a variety of operating conditions such as inducer concentration and dilution rate. This model is useful for understanding the behavior of two-stage continuous cultures. (c) 1993 John Wiley & Sons, Inc.     

Dynamic model development for a continuous culture of Saccharomyces cerevisiae

The problem of dynamically modeling a chemostat is addressed. Using the results of continuous culture experiments for the growth of a strain of Saccharomyces cerevisiae on a glucose-limited medium, a general approach to developing dynamic models is discussed. The approach to develop and verify the model involves three different types of experiments: steady-state, dynamic step response, and feedback identification.     

Model for the feedback control system of bacterial growth. II. Growth in continuous culture

A mathematical model is developed that describes substrate limited bacterial growth in a continuous culture and that is based upon the conceptual framework elaborated in a previous paper for describing the feedback control system of cell growth [S. Bleecken, (1988). J. theor. Biol. 133, 37.] Central to the theory are the ideas that the limiting substrate is converted into low molecular weight building blocks of macromolecular synthesis which again are converted into biomass (RNA and protein) and that the rates of RNA and protein synthesis are controlled by the intracellular concentration of building blocks. It is shown that a continuous culture can be simulated by two interconnected feedback control systems the actuating signals of which are limiting substrate concentration and the intracellular concentration of building blocks, respectively. Three types of steady-states are found to appear in a continuous culture, besides the well-known stable steady-state of the whole culture there exist two batchlike steady-states of the biotic part of the culture which are metastable. The model is used to analyse the steady-states and their stability properties as well as the dynamic responses of biomass, RNA, protein, building block and substrate concentrations to changes in environmental conditions. Especially the inoculation of a continuous culture and the effects of step changes in dilution rate, inlet substrate concentration and growth temperature are studied in detail. Relations between the growth behaviour of a single cell and that of a continuous culture are derived. The RNA to protein ratio is introduced as a rough measure of the physiological state of cells and it is shown that a cell reacts to environmental changes with a simple pattern of basic responses in growth rate and physiological state. There are reasons to assume that the model presented is the minimal version of a structured model of bacterial growth and represents an optimum compromise between biological relevance and mathematical practicability.     

Structural sensitivity of grazing formulations in nutrient controlled plankton models

Summary Stability and persistence properties of a family of non-spatial plankton models, each differentiated by its herbivore grazing term, are analytically compared. The dynamic persistence function in the model is shown to operate uniformly even though stability configuration characteristics of the model may be topologically distinct. The persistence threshold for each model indicates that total nutrient is a fundamental biological control. In the parameter space, all of the models studied are structurally unstable; however, an important bifurcation mechanism associated with this instability governs persistence. While, topologically, model transfigurement through parameter modulation is non-continuous, the biological populations evolve in a continuous or a lower semicontinuous manner. A basic conclusion of the paper is that fundamental problems for these marine ecological models remain unresolved since each of the models is a structurally unstable system for a fixed dynamically persistent ecology.     

An NIR-based PAT approach for real-time control of loading in Protein A chromatography in continuous manufacturing of monoclonal antibodies

Control of column loading in Protein A chromatography is a crucial part of development of robust and flexible process platforms for continuous production of monoclonal antibody (mAb) products. In this paper, we propose a control system that uses near infrared spectroscopy (NIRS) flow cells to accomplish the above. Two applications have been demonstrated using a periodic counter-current continuous chromatography setup. The first application involves use of single NIR flow cell before the inlet of the loading column to measure the concentration of mAb in the harvested broth. Measurement was in real-time (every 3 s) and within ±0.05 mg/ml, significantly better than making UV-based concentration estimations. The second application involved use of an additional NIR flow cell at the outlet of the loading column to measure column breakthrough in real time. The concentration data was transferred to a Python-based monitoring and control algorithm layered over a Cadence BioSMB system. The program could successfully run a three-column periodic counter current method on the BioSMB whereas controlling loading to ensure optimal resin utilization in each loading cycle phase based on precharacterized dynamic binding capacity models, whereas maintaining periodic elutions. The system was tested with multiple perturbations in harvest concentration, modeled after deviations that could arise downstream of a perfusion cell culture system. The results show that the proposed control is a spectroscopy-based process analytical technology tool that facilitates real time monitoring and control of loading in process chromatography. It is adaptable to any continuous chromatography equipment and is very well suited for implementation in a continuous mAb production train.     

Robust model matching control of immune systems under environmental disturbances: dynamic game approach

A robust model matching control of immune response is proposed for therapeutic enhancement to match a prescribed immune response under uncertain initial states and environmental disturbances, including continuous intrusion of exogenous pathogens. The worst-case effect of all possible environmental disturbances and uncertain initial states on the matching for a desired immune response is minimized for the enhanced immune system, i.e. a robust control is designed to track a prescribed immune model response from the minimax matching perspective. This minimax matching problem could herein be transformed to an equivalent dynamic game problem. The exogenous pathogens and environmental disturbances are considered as a player to maximize (worsen) the matching error when the therapeutic control agents are considered as another player to minimize the matching error. Since the innate immune system is highly nonlinear, it is not easy to solve the robust model matching control problem by the nonlinear dynamic game method directly. A fuzzy model is proposed to interpolate several linearized immune systems at different operating points to approximate the innate immune system via smooth fuzzy membership functions. With the help of fuzzy approximation method, the minimax matching control problem of immune systems could be easily solved by the proposed fuzzy dynamic game method via the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. Finally, in silico examples are given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed method.     

A computer based culturing system for measuring the photosynthetic response of phytoplankton to a fluctuating environment

A microcomputer-controlled culturing system developed to simulate temperature and salinity fluctuations in an estuary is described. The system consists of a microcomputer, interfacing hardware, a continuous culture apparatus, and system software. The system can regulate the temperature and salinity of a continuous phytoplankton culture based on user-defined models of the physical environment and particle transport in a natural environment. The microcomputer also provides efficient data acquisition and data storage. The system was designed to facilitate expansion and modification and can easily be adapted to accomodate various studies of phytoplankton production. Details of a simulation and representative data are presented.     

Metabolic modeling of Saccharomyces cerevisiae using the optimal control of homeostasis: a cybernetic model definition

A model is presented to describe the observed behavior of microorganisms that aim at metabolic homeostasis while growing and adapting to their environment in an optimal way. The cellular metabolism is seen as a network with a multiple controller system with both feedback and feedforward control, i.e., a model based on a dynamic optimal metabolic control. The dynamic network consists of aggregated pathways, each having a control setpoint for the metabolic states at a given growth rate. This set of strategies of the cell forms a true cybernetic model with a minimal number of assumptions. The cellular strategies and constraints were derived from metabolic flux analysis using an identified, biochemically relevant, stoichiometry matrix derived from experimental data on the cellular composition of continuous cultures of Saccharomyces cerevisiae. Based on these data a cybernetic model was developed to study its dynamic behavior. The growth rate of the cell is determined by the structural compounds and fluxes of compounds related to central metabolism. In contrast to many other cybernetic models, the minimal model does not consist of any assumed internal kinetic parameters or interactions. This necessitates the use of a stepwise integration with an optimization of the fluxes at every time interval. Some examples of the behavior of this model are given with respect to steady states and pulse responses. This model is very suitable for describing semiquantitatively dynamics of global cellular metabolism and may form a useful framework for including structured and more detailed kinetic models.     

Experimental adaptive on-line optimization of cellular productivity of a continuous bakers' yeast culture

An adaptive on-line optimization method that utilizes dynamic model identification has been applied to maximize the cellular productivity of a continuous bakers' yeast culture. Experiments were conducted on a sophisticated computerized fermentation system. Experimental results show that the adaptive on-line optimization method requires very little a priori information, is easy to implement, converges quickly, adapts to changes in the process, and is stable even when operational difficulties are encountered.     

Automated fermentation equipment I. program-controlled fermentor

A fermentation system with a plug scheme unit has been developed, offering a variety of solutions to measurement, control, and operational problems. By means of the program unit, e.g., automatic pH control assigned to the dynamic of batch cultures and the feed of different ingredients controlled by a time program or a given variable have been solved. The continuous culture volume was controlled by a level controlled by a level controller equipped with a photosensor. A method was developed for variable control that provide information on the activity of the culture, and allows direct measurement of the different rate values, e.g., generation time or specific product formation rate. Applicability of the direct measurement of generation time is presented in the qualification of molasses and in a static off-line optimization process.     

μ-Synthesis of dissimilation process of glycerol to 1,3-propanediol in microbial continuous culture

In this paper, robust control problem using μ-synthesis in microbial continuous culture is studied. The dissimilation process of glycerol to 1,3-propanediol cannot avoid the disturbances caused by uncertain factors. Based on the biodynamical model, a control system with the initial glycerol concentration as input control is proposed to simplify the controller design. μ-synthesis method is applied to find a feedback controller to assure both of robust stability and robust performance of the closed-loop system simultaneously. To solve the corresponding structured singular value optimization problem, a converged result is obtained through D–K iteration method. The μ-synthesis system is also compared with the corresponding $H_\infty$ system. The simulation results indicate that the μ-controller might be more feasible for the continuous bioprocess controlling.     

Two Monthly Continuous Dynamic Model Based on Nash Bargaining Theory for Conflict Resolution in Reservoir System

So far many optimization models based on Nash Bargaining Theory associated with reservoir operation have been developed. Most of them have aimed to provide practical and efficient solutions for water allocation in order to alleviate conflicts among water users. These models can be discussed from two viewpoints: (i) having a discrete nature; and (ii) working on an annual basis. Although discrete dynamic game models provide appropriate reservoir operator policies, their discretization of variables increases the run time and causes dimensionality problems. In this study, two monthly based non-discrete optimization models based on the Nash Bargaining Solution are developed for a reservoir system. In the first model, based on constrained state formulation, the first and second moments (mean and variance) of the state variable (water level in the reservoir) is calculated. Using moment equations as the constraint, the long-term utility of the reservoir manager and water users are optimized. The second model is a dynamic approach structured based on continuous state Markov decision models. The corresponding solution based on the collocation method is structured for a reservoir system. In this model, the reward function is defined based on the Nash Bargaining Solution. Indeed, it is used to yield equilibrium in every proper sub-game, thereby satisfying the Markov perfect equilibrium. Both approaches are applicable for water allocation in arid and semi-arid regions. A case study was carried out at the Zayandeh-Rud river basin located in central Iran to identify the effectiveness of the presented methods. The results are compared with the results of an annual form of dynamic game, a classical stochastic dynamic programming model (e.g. Bayesian Stochastic Dynamic Programming model, BSDP), and a discrete stochastic dynamic game model (PSDNG). By comparing the results of alternative methods, it is shown that both models are capable of tackling conflict issues in water allocation in situations of water scarcity properly. Also, comparing the annual dynamic game models, the presented models result in superior results in practice. Furthermore, unlike discrete dynamic game models, the presented models can significantly reduce the runtime thereby avoiding dimensionality problems.     

Control strategies of continuous bioprocesses based on biological activities

Based on the material balance principle applied to microbial reactions in continuous bioprocesses, the concept of reaction rate control has been developed theoretically. This concept provides a more direct way of controlling biological activities than the control of physical or chemical parameters in practice today. From an analysis of dynamic and steady-state experiments, two control systems for carbon dioxide production rate control during the continuous culture of baker's yeast have been designed and evaluated experimentally. In these control methods, intracellular NADH concentration is used as an immediate indication of the onset of glucose repression. A more sophisticated master controller based on the respiratory quotient can be combined with these control methods. The resulting control system provides a means to indirectly optimize biomass production while preventing ethanol formation in the continuous culture of baker's yeast.     

Dynamics of microbial propagation: Models considering inhibitors and variable cell composition

Mathematical models for microbial growth in batch and continuous cultures are formulated. The models have been referred to as distributed models since the microbial population in a culture is looked upon as protoplasmic mass distributed uniformly throughout the culture. Growth is regarded as the increase in this mass by conversion of medium components into biological mass and metabolic products. Two sets of models have been presented. The first arise from introducing additional considerations into the model proposed by Monod to account for the stationary phase and the phase of decline in a batch culture. These have been referred to as unstructured, distributed models since they do not recognize any form of structure in the protoplasmic mass. The models in the second set are referred to as structured, distributed models. Structure is introduced by considering the protoplasmic mass to be composed of two groups of substances which interact with each other and with substances in the environment to produce growth. The structured models account for the dependence of growth on the past, history of the cells; thus they predict all growth phases observed in batch cultures, whereas the unstructured models do not predict a lag phase. The full implications of the models for continuous propagation, as determined by the method of stability analysis and transient calculations, are discussed. The models prediet a number of new results and should be confronted with experiments.     

A multi-phase optimal control technique for the simulation of a human vertical jump

A multi-phase optimal control technique is presented that can be used to solve dynamic optimization problems involving musculoskeletal systems. The biomechanical model consists of a set of differential equations describing the dynamics of the multi-body system and the generation of the dynamic forces of the human muscles. Within the optimization technique, subintervals can be defined in which the differential equations are continuous. At the boundaries the dimension of the state- and control vector as well as the dimension of the right-hand side may change. The problem is solved by a multiple shooting approach which converts the problem into a non-linear program. The method is applied to simulate a human jump movement.     

Reverse engineering: the architecture of biological networks

We adopt a control theory approach to reverse engineer the complexity of a known system--the bacterial heat shock response. Using a computational dynamic model, we explore the organization of the heat shock system and elucidate its various regulation strategies. We show that these strategies are behind much of the complexity of the network. We propose that complexity is a necessary outcome of robustness and performance requirements that are achieved by the heat shock system's exquisite regulation modules. The techniques we use rely on dynamic computational models and principles from the field of control theory.     

The Continuous Culture of Luminous Bacteria: a Luminostat

A method has been designed for the continuous culture of luminous bacteria. The control system for the culture uses a combination of luminescence and optical density as a light signal received by a photomultiplier. This combined signal operates pumps which exchange the growth medium. Using this method, a culture of brightly luminescing bacteria was maintained for periods up to 3 weeks.     

Multilevel control of multistage continuous culture using a microprocessor

This paper describes the implementation of multilevel techniques using a microprocessor to control multistage continuous culture systems. A system which produces gramicidin S is taken as an example. The single level technique using the conjugate gradient method is applied to solve the two-stage and the three-stage continuous culture and is compared with the multilevel one. The results show that the application of multilevel techniques is more advantageous and suitable for this system than any other method which has been utilized so far. The advantages of using a microprocessor will be stated.