Optimal fed batch experiment design for estimation of monod kinetics of Azospirillum brasilense: from theory to practice

In this paper the problem of reliable and accurate parameter estimation for unstructured models is considered. It is illustrated how a theoretically optimal design can be successfully translated into a practically feasible, robust, and informative experiment. The well-known parameter estimation problem of Monod kinetic parameters is used as a vehicle to illustrate our approach. As known for a long time, noisy batch measurements do not allow for unique and accurate estimation of the kinetic parameters of the Monod model. Techniques of optimal experiment design are, therefore, exploited to design informative experiments and to improve the parameter estimation accuracy. During the design process, practical feasibility has to be kept in mind. The designed experiments are easy to implement in practice and do not require additional monitoring equipment. Both design and experimental validation of informative fed batch experiments are illustrated with a case study, namely, the growth of the nitrogen-fixing bacteria Azospirillum brasilense.     

Dynamic fuzzy model based predictive controller for a biochemical reactor

The kinetics of bioreactions often involve some uncertainties and the dynamics of the process vary during the course of fermentation. For such processes, conventional control schemes may not provide satisfactory control performance and demands extra effort to design advanced control schemes. In this study, a dynamic fuzzy model based predictive controller (DFMBPC) is presented for the control of a biochemical reactor. The DFMBPC incorporates an adaptive fuzzy modeling framework into a model based predictive control scheme to derive analytical controller output. The DFMBPC has the flexibility to opt with various types of fuzzy models whose choice also lead to improve the control performance. The performance of DFMBPC is evaluated by comparing with a fuzzy model based predictive controller (FMBPC) with no model adaptation and a conventional PI controller. The results show that DFMBPC provides better performance for tracking setpoint changes and rejecting unmeasured disturbances in the biochemical reactor.     

An unstructured model for studies on phenanthrene bioconversion by filamentous fungus Cunninghamella elegans

An unstructured model for phenanthrene bioconversion by filamentous fungus Cunnighamella elegans in stirred tank batch bioreactors was proposed. It was observed that the process of phenanthrene bioconversion is strictly associated with exponential growth of biomass. Therefore, a Monod-type, with Contois term, unstructured model could be applied to describe the process mathematically. The inhibition of biomass growth due to high concentrations of phenanthrene present in the medium was taken into account in the form of Yerusalimski's uncompetitive inhibition term.     

Process performance models in the optimization of multiproduct protein production plants

In this work we propose a model that simultaneously optimizes the process variables and the structure of a multiproduct batch plant for the production of recombinant proteins. The complete model includes process performance models for the unit stages and a posynomial representation for the multiproduct batch plant. Although the constant time and size factor models are the most commonly used to model multiproduct batch processes, process performance models describe these time and size factors as functions of the process variables selected for optimization. These process performance models are expressed as algebraic equations obtained from the analytical integration of simplified mass balances and kinetic expressions that describe each unit operation. They are kept as simple as possible while retaining the influence of the process variables selected to optimize the plant. The resulting mixed-integer nonlinear program simultaneously calculates the plant structure (parallel units in or out of phase, and allocation of intermediate storage tanks), the batch plant decision variables (equipment sizes, batch sizes, and operating times of semicontinuous items), and the process decision variables (e.g., final concentration at selected stages, volumetric ratio of phases in the liquid-liquid extraction). A noteworthy feature of the proposed approach is that the mathematical model for the plant is the same as that used in the constant factor model. The process performance models are handled as extra constraints. A plant consisting of eight stages operating in the single product campaign mode (one fermentation, two microfiltrations, two ultrafiltrations, one homogenization, one liquid-liquid extraction, and one chromatography) for producing four different recombinant proteins by the genetically engineered yeast Saccharomyces cerevisiae was modeled and optimized. Using this example, it is shown that the presence of additional degrees of freedom introduced by the process performance models, with respect to a fixed size and time factor model, represents an important development in improving plant design.     

Robust operation of fed batch fermenters

Optimisation of fed batch fermenters can substantially increase the profitability of these processes. Optimal control of a fed batch fermenter is usually based on a nominal process model. Parameter uncertainties are not taken into account. Simulation studies show that results obtained with fixed nominal model parameters can be quite sensitive to the uncertainty in parameter values. This paper presents a method for obtaining robust optimal control profiles in the presence of uncertainty in the model parameters. The proposed approach is illustrated with a case study. It is also shown that feedback controllers can reduce the effect of the uncertainties.     

Analytical fuzzy approach to biological data analysis

The assessment of the physiological state of an individual requires an objective evaluation of biological data while taking into account both measurement noise and uncertainties arising from individual factors. We suggest to represent multi-dimensional medical data by means of an optimal fuzzy membership function. A carefully designed data model is introduced in a completely deterministic framework where uncertain variables are characterized by fuzzy membership functions. The study derives the analytical expressions of fuzzy membership functions on variables of the multivariate data model by maximizing the over-uncertainties-averaged-log-membership values of data samples around an initial guess. The analytical solution lends itself to a practical modeling algorithm facilitating the data classification. The experiments performed on the heartbeat interval data of 20 subjects verified that the proposed method is competing alternative to typically used pattern recognition and machine learning algorithms.     

Individual-based modeling of phytoplankton: evaluating approaches for applying the cell quota model

Present phytoplankton models typically use a population-level (lumped) modeling (PLM) approach that assumes average properties of a population within a control volume. For modern biogeochemical models that formulate growth as a nonlinear function of the internal nutrient (e.g. Droop kinetics), this averaging assumption can introduce a significant error. Individual-based (agent-based) modeling (IBM) does not make the assumption of average properties and therefore constitutes a promising alternative for biogeochemical modeling. This paper explores the hypothesis that the cell quota (Droop) model, which predicts the population-average specific growth or cell division rate, based on the population-average nutrient cell quota, can be applied to individual algal cells and produce the same population-level results. Three models that translate the growth rate calculated using the cell quota model into discrete cell division events are evaluated, including a stochastic model based on the probability of cell division, a deterministic model based on the maturation velocity and fraction of the cell cycle completed (maturity fraction), and a deterministic model based on biomass (carbon) growth and cell size. The division models are integrated into an IBM framework (iAlgae), which combines a lumped system representation of a nutrient with an individual representation of algae. The IBM models are evaluated against a conventional PLM (because that is the traditional approach) and data from a number of steady and unsteady continuous (chemostat) and batch culture laboratory experiments. The stochastic IBM model fails the steady chemostat culture test, because it produces excessive numerical randomness. The deterministic cell cycle IBM model fails the batch culture test, because it has an abrupt drop in cell quota at division, which allows the cell quota to fall below the subsistence quota. The deterministic cell size IBM model reproduces the data and PLM results for all experiments and the model parameters (e.g. maximum specific growth rate, subsistence quota) are the same as those for the PLM. In addition, the model-predicted cell age, size (carbon) and volume distributions are consistent with those derived analytically and compare well to observations. The paper discusses and illustrates scenarios where intra-population variability in natural systems leads to differences between the IBM and PLM models.     

Unstructured model for L-lysine fermentation under controlled dissolved oxygen

An unstructured model was developed for batch cultivation of Corynebacterium lactofermentum (ATCC 21799) under controlled dissolved oxygen. The model is capable of predicting batch experiments performed at various initial substrate concentrations. By extending the batch culture model to a fed-batch model and using a heuristic approach to optimize the fed-batch cultivation, it is shown that fed-batch cultivation is superior to batch operation due to increased productivity at high substrate concentrations.     

Controlling the time evolution of mAb N‐linked glycosylation ‐ Part II: Model‐based predictions

N‐linked glycosylation is known to be a crucial factor for the therapeutic efficacy and safety of monoclonal antibodies (mAbs) and many other glycoproteins. The nontemplate process of glycosylation is influenced by external factors which have to be tightly controlled during the manufacturing process. In order to describe and predict mAb N‐linked glycosylation patterns in a CHO‐S cell fed‐batch process, an existing dynamic mathematical model has been refined and coupled to an unstructured metabolic model. High‐throughput cell culture experiments carried out in miniaturized bioreactors in combination with intracellular measurements of nucleotide sugars were used to tune the parameter configuration of the coupled models as a function of extracellular pH, manganese and galactose addition. The proposed modeling framework is able to predict the time evolution of N‐linked glycosylation patterns during a fed‐batch process as a function of time as well as the manipulated variables. A constant and varying mAb N‐linked glycosylation pattern throughout the culture were chosen to demonstrate the predictive capability of the modeling framework, which is able to quantify the interconnected influence of media components and cell culture conditions. Such a model‐based evaluation of feeding regimes using high‐throughput tools and mathematical models gives rise to a more rational way to control and design cell culture processes with defined glycosylation patterns. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1135–1148, 2016     

Monitoring of a sequencing batch reactor using adaptive multiblock principal component analysis

Multiway principal component analysis (MPCA) for the analysis and monitoring of batch processes has recently been proposed. Although MPCA has found wide applications in batch process monitoring, it assumes that future batches behave in the same way as those used for model identification. In this study, a new monitoring algorithm, adaptive multiblock MPCA, is developed. The method overcomes the problem of changing process conditions by updating the covariance structure recursively. A historical set of operational data of a multiphase batch process was divided into local blocks in such a way that the variables from one phase of a batch run could be blocked in the corresponding blocks. This approach has significant benefits because the latent variable structure can change for each phase during the batch operation. The adaptive multiblock model also allows for easier fault detection and isolation by looking at the relationship between blocks and at smaller meaningful block models, and it therefore helps in the diagnosis of the disturbance. The proposed adaptive multiblock monitoring method is successfully applied to a sequencing batch reactor for biological wastewater treatment.     

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.     

Physiological state control of fermentation processes

In this article a novel approach to the control of fermentation processes is introduced. A "physiological state control approach" has been developed using the concept of representing fermentation processes through the current physiological state of the cell culture. No conventional mathematical model is required for the synthesis of such a control system.The main idea is based on the fact that during batch, feed-batch, or even continuous cultivation the physiological characteristics of the cell population, jointly expressed by the term "physiological state", are not constant but rather variable, which is reflected in expected or unexpected changes in the behavior of the control plant, and which requires flexible alteration of the current control strategy. The proposed approach involves decomposition of the physiological state space into several subspaces called "physiological situations." In every physiological situation the cell population expresses stable characteristics, and therefore an invariant control strategy can be effectively applied. The on-line functions of the physiological state control system consist of the calculation of physiological state variables, determination of the current physiological situation as an element of a previously defined set of known physiological situations, switching of the relevant control strategy, and calculation of the control action. Attention is focused on the synthesis of the novel and nonstandard part of the control system - the algorithm for online recognition of the current physiological state. To this end an effective approach, based on artificial intelligence methods, particularly fuzzy sets theory and pattern recognition theory, was developed. Its practical realization is demonstrated using data from a continuous fermentation process for single cell protein production.     

Variable selection in nonlinear modeling based on RBF networks and evolutionary computation

In this paper a novel variable selection method based on Radial Basis Function (RBF) neural networks and genetic algorithms is presented. The fuzzy means algorithm is utilized as the training method for the RBF networks, due to its inherent speed, the deterministic approach of selecting the hidden node centers and the fact that it involves only a single tuning parameter. The trade-off between the accuracy and parsimony of the produced model is handled by using Final Prediction Error criterion, based on the RBF training and validation errors, as a fitness function of the proposed genetic algorithm. The tuning parameter required by the fuzzy means algorithm is treated as a free variable by the genetic algorithm. The proposed method was tested in benchmark data sets stemming from the scientific communities of time-series prediction and medicinal chemistry and produced promising results.     

Segregated mathematical model for growth of anchorage-dependent MDCK cells in microcarrier culture

To describe the growth behavior of anchorage-dependent mammalian cells in microcarrier systems, various approaches comprising deterministic and stochastic single cell models as well as automaton-based models have been presented in the past. The growth restriction of these often contact-inhibited cells by spatial effects is described at levels with different complexity but for the most part not taking into account their metabolic background. Compared to suspension cell lines these cells have a comparatively long lag phase required for attachment and start of proliferation on the microcarrier. After an initial phase of exponential growth only a moderate specific growth rate is achieved due to restrictions in space available for cell growth, limiting medium components, and accumulation of growth inhibitors. Here, a basic deterministic unstructured segregated cell model for growth of Madin Darby Canine Kidney (MDCK) cells used in influenza vaccine production is described. Four classes of cells are considered: cells on microcarriers, cells in suspension, dead cells, and lysed cells. Based on experimental data, cell attachment and detachment is taken explicitly into account. The model allows simulation of the overall growth behavior in microcarrier culture, including the lag phase. In addition, it describes the time course of uptake and release of key metabolites and the identification of parameters relevant for the design and optimization of vaccine manufacturing processes.     

Morphologically structured model for antitumoral retamycin production during batch and fed-batch cultivations of Streptomyces olindensis

A morphologically structured model is proposed to describe trends in biomass growth, substrate consumption, and antitumoral retamycin production during batch and fed-batch cultivations of Streptomyces olindensis. Filamentous biomass is structured into three morphological compartments (apical, subapical, and hyphal), and the production of retamycin, a secondary metabolite, is assumed to take place in the subapical cell compartment. Model accounts for the effect of glucose as well as complex nitrogen source on both the biomass growth and retamycin production. Laboratory data from bench-scale batch and fed-batch fermentations were used to estimate some model parameters by nonlinear regression. The predictive capability of the model was then tested for additional fed-batch and continuous experiments not used in the previous fitting procedure. The model predictions show fair agreement to the experimental data. The proposed model can be useful for further studies on process optimization and control.     

Mathematical modeling for mixed culture growth of two bacterial populations with opposite substrate preferences

An unstructured mathematical model is proposed for mixed culture growth of two different bacterial species that exhibit "opposite" substrate preferences in response to the "same" environmental conditions. The model incorporates enzymatic control mechanisms such as induction, repression, and inhibition in the microorganisms as manifested in their preferential utilization of substrates and microbial interactions such as amensalism and competition. The model predicts cell mass, substrate concentrations, dissolved oxygen tension, as well as key enzyme levels. The predictions of the model are compared with experimental data for pure culture growth and for mixed culture growth on two substrates, glucose and citrate, in a batch reactor.     

Nonlinear biological batch process monitoring and fault identification based on kernel fisher discriminant analysis

A novel nonlinear biological batch process monitoring and fault identification approach based on kernel Fisher discriminant analysis (kernel FDA) is proposed. This method has a powerful ability to deal with nonlinear data and does not need to predict the future observations of variables. So it is more sensitive to fault detection. In order to improve the monitoring performance, variable trajectories of the batch processes are separated into several blocks. Then data in the original space is mapped into high-dimensional feature space via nonlinear kernel function and the optimal kernel Fisher feature vector and discriminant vector are extracted to perform process monitoring and fault identification. The key to the proposed approach is to calculate the distance of block data which are projected to the optimal kernel Fisher discriminant vector between new batch and reference batch. Through comparing distance with the predefined threshold, it can be considered whether the batch is normal or abnormal. Similar degree between the present discriminant vector and the optimal discriminant vector of fault in historical data set is used to perform fault diagnosis. The proposed method is applied to the process of fed-batch penicillin fermentation simulator benchmark and shows that it can effectively capture nonlinear relationships among process variables and is more efficient than MPCA approach.     

A deterministic model for monophasic growth of batch cultures of bacteria

Experimental observations of bacterial numbers employing high resolution electrical conductance measurements of the culture provide the basis for a proposed deterministic model of monophasic growth of populations in batch culture. The model postulates that the production and growth of each bacterium is accompanied by the generation of a constant mass of toxic end-products and that specific growth rate declines in proportion to the ratio of the accumulated mass of these substances to the dry mass of the nutrient medium when the substrate is non-limiting. The theoretical relationship is found to fit extensive data for Escherichia coli (NCIB 9132) very closely and offers an analytical basis for the logistic curve frequently observed to represent the time-dependence of growth. These data incidentally provide substantial evidence that lag time and generation time are each independent of both inoculum number and concentration of the medium.