Optimal Feeding Profile Research Articles

Optimizing Fed-Batch Processes with Dynamic Control Flux Balance Analysis

Fed-batch processes are prevalent in biotechnological industries, but design of experiments often results in sub-optimal conditions due to incomplete solution space characterization. We employ a single-level dynamic control (DC) algorithm for dynamic flux balance analysis (dFBA), enhancing efficiency by reducing Karush-Kuhn-Tucker (KKT) condition constraints and adapting the algorithm for predicting optimal process length. In a growth-decoupled plasmid DNA production case study, we predict the optimal feeding profile and switching time between growth and production phase. Comparing our algorithm to its predecessor shows a speed-up of at least a factor of four. When the process length is part of the objective function the speed-up becomes considerably larger.

Insertion of ester bonds in three terpolymerization systems

Nonbiodegradable (co)polymers with all-carbon backbone produced via radical polymerization are used in various applications. For some applications, like for example in skincare and haircare, these polymers are nonrecoverable and therefore would be preferably made biodegradable. Therefore, inserting ester bonds in the backbone via radical ring opening terpolymerization of acrylates and 2-methylene-1,3 dioxepane (MDO) could be a suitable approach to obtain biodegradable terpolymers. This report investigates the influence of batch versus semibatch process on the polymerization of three terpolymerization systems viz. (i) methacrylamide (MAAM)/n-butyl acrylate (nBA)/BMDO (5,6-Benzo-2-Methylene-1,3-Dioxepane), (ii) MAAM/nBA/MDO, and (iii) methyl methacrylate (MMA)/VAc (vinyl acetate) /MDO. We demonstrate the improvement in number of ester groups inserted and the homogeneity of insertion via semibatch polymerization processes. The process is guided via optimal monomer addition feeding profiles generated using the reactivity ratios of comonomers. Such improved insertion was demonstrated by the molecular weight distribution of fragments after alkali degradation in the investigated systems.

β-glucosidase production by recombinant Pichia pastoris strain Y1433 under optimal feed profiles of fed-batch cultivation.

Pichia pastoris, a methylotrophic yeast, is known to be an efficient host for heterologous proteins production. In this study, a recombinant P. pastoris Y11430 was found better for β-glucosidase activity in comparison with a wild type P. pastoris Y11430 strain, and thereby, subjected to methanol intermittent feed profiling for β-glucosidase production. The results showed that at 72h of cultivation time, the cultures with 16.67% and 33.33% methanol feeding with constant rate could produce the total dry cell weight of 52.23 and 118.55g/L, respectively, while the total mutant β-glucosidase activities were 1001.59 and 3259.82 units, respectively. The methanol feeding profile was kept at 33% with three methanol feeding strategies such as constant feed rate, linear feed rate, and exponential feed rate which were used in fed-batch fermentation. At 60h of cultivation, the highest total mutant β-glucosidase activity was 2971.85 units for exponential feed rate culture. On the other hand, total mutant β-glucosidase activity of the constant feed rate culture and linear feed rate culture were 1682.25 and 1975.43 units, respectively. The kinetic parameters of exponential feed rate culture were specific growth rate on glycerol 0.228/h, specific growth of methanol 0.061/h, maximum total dry cell weight 196.73g, yield coefficient biomass per methanol ([Formula: see text]) 0.57 gcell/gMeOH, methanol consumption rate ([Formula: see text]) 5.76 gMeOH/h, and enzyme productivity ([Formula: see text]) 75.96 units/h. In conclusion, higher cell mass and β- glucosidase activity were produced under exponential feed rate than constant and linear feed rates.

Robust Multi-Objective Singular Optimal Control Ofpenicillin Fermentation Process

The determination of optimal feeding profile of fed-batch fermentation requires the solution of a singular optimal control problem. The complexity in obtaining the solution to this singular problem is due to the nonlinear dynamics of the system model, the presence of control variables in linear form and the existence of constraints in both the state and control variables. Traditionally, during the optimization process, uncertainties associated with design variables, control parameters and mathematical model are not considered. In this contribution, a systematic methodology to evaluate uncertainties during the resolution of a singular optimal control problem is proposed. This approach consists of the Multi-objective Optimization Differential Evolution algorithm associated with Effective Mean Concept. The proposed methodology is applied to determine the feed substrate concentration in fed-batch penicillin fermentation process. The robust multi- objective singular optimal control problem consists of maximizing the productivity and minimizing the operation total time.

Dynamic optimization of fed-batch bioprocesses using flower pollination algorithm.

There exist several optimization strategies such as sequential quadratic programming (SQP), iterative dynamic programing (IDP), stochastic-based methods such as differential evolution (DE), genetic algorithm (GA), particle swarm optimization (PSA), and ant colony optimization (ACO) for finding optimal feeding profile(s) during fed-batch fermentations. Here in the present study, flower pollination algorithm (FPA) which is inspired by the pollination process in terrestrial flowering plants has been used for the first time to find the optimal feeding profile(s) during fed-batch fermentations. Single control variable, two control variables and state variable bounded problems were chosen to test the robustness of the FPA for optimal control problems. It was observed that FPA is computationally less intensive in comparison with other stochastic strategies. Thus, obtained results were compared to other studies and it has been found that the FPA converged either to newer optima or closer to the established global optimum for the cases studied.

Harmonic multi-objective differential evolution approach for multi-objective optimization of fed-batch bioreactor

ABSTRACTLysine as one of the essential amino acids is often used as a chemical agent, medicament, food material, and human and animals feed additive. Microbial fermentation is one of the most economical processes to produce lysine. Batch or fed-batch fermentation processes are often used to produce lysine. The use of fed-batch operation improves the productivity, reduces the fermentation time, and increases the yield of the reaction. Using a mathematical modeling approach, it is possible to obtain a deeper insight of biochemical-based processes. In this manuscript, an optimal feeding profile for fed-batch bioreactor is obtained for the multi-objective optimization (MOO) of conflicting objectives, i.e., the yield (with two different expressions) and the productivity. MODE-III and Harmonic MODE algorithms are used for the MOO study. Pareto optimal fronts are also reported for constant feeding rate, singular feeding rates, and for the different feeding rates in a given range. With the increase in the value of the feed rate, the productivity increases while the yield decreases. Both versions of the MODE algorithm result in the smooth Pareto front; however, the Harmonic MODE algorithm results in a good and diverse set of solutions.

Optimal feed profile for the Rhamnolipid kinetic models by using Tabu search: metabolic view point.

Rhamnolipids are bio surfactants which are extra-cellular glycolipids composed of l-rhamnose and 3-hydroxyalkanoics. Rhamnolipids are produced through fermentation process by using Pseudomonas sp. as the species. An alteration to the traditional procedures in order to achieve increase in the production of biosurfactants, a numerous process technologies have been adopted in fed batch mode. Fed batch mode facilitates the high production of product by avoiding the substrate or product inhibition line of attack. To overcome the controlling parameters which reduce the product yield, optimal control profiles are designed. In order to develop viable control methods for fed-batch fermentation of Rhamnolipid production, multiple substrate feeding strategies were employed and their efficiencies were compared with different substrates concentration of glucose, nitrogen and phosphorous. The product formation depends upon the substrate feeding strategy and so, the fed-batch fermentation was carried out by using P. aeruginosa providing substrates at manifold rates. With the obtained experimental data, using the kinetic models (logistic equation and by Luedeking Piret), the kinetic parameters were estimated. These kinetic parameters were implemented in tabu search algorithm and this programme was executed in Dev-C++, optimal control profiles were generated as a result. These obtained optimal control profiles have shown an increase in productivity of rhamnolipid with a decline in computational time. Through this procedure, the optimal control profiles of substrate feeding strategies of glucose, nitrogen and phosphorous were estimated. In comparison with other algorithms like genetic algorithm, Tabu Search algorithm was able to generate an accurate optimal control profiles with a reduction in their intricacy.

An Integrated Biorefinery Framework for the Coproduction of Biofuels and Chemicals: Experimental Analysis, Detailed Modelling, Optimization and Life Cycle Analysis

In this work, a novel integrated biorefinery framework is introduced. A ?cradle to grave? analysis is developed by adding novel steps into a basic biodiesel process involving the valorization of waste streams to value-added chemicals. Insights are given towards a new bioconversion route of glycerol to succinic acid. An unstructured model of batch experiments at different conditions is constructed. Experimental results at the bench scale are used to estimate kinetic parameters and to validate model predictions. The developed model is used in optimization studies to compute the best initial conditions for batch as well as the optimal feeding profiles for fed-batch processes to maximize succinic acid productivity. Finally, the above process is incorporated into a biorefinery scheme. Simulation and optimization in conjunction with life cycle analysis (LCA) is performed to simultaneously improve its sustainability and its economics.

Thermal Process Safety Based on Reaction Kinetics and Reactor Dynamics

The specific problem of non-converted reactant accumulation encountered in fed-batch reactor is a challenging task of process safety. In order to avoid such situation that may lead to a runaway reaction, the reaction kinetics and reactor dynamic must be known. In this work, an innovative approach to determine an optimal feed profile, based on a reaction kinetic and reactor dynamic, is presented. This approach was applied to the reaction system involved in the Morton International Inc. incident. Great improvements were observed in the control of the accumulation, decreasing the number of necessary experiments needed for the scale-up studies.

A new approach for finding smooth optimal feeding profiles in fed-batch fermentations

In this work, a new approach for smooth control profiles parameterization (requiring a small number of parameters) is presented and especially recommended for bioprocess applications because of the smoothness of the profiles obtained, which are not only continuous time functions but also differentiable along the whole control interval. The importance of smooth profiles relays on the fact that abrupt changes in the cells’ environment may affect the metabolism of the cell, usually leading to a decrease in the process productivity. The parameterization proposed in this work is based on sinusoidal functions, which not only describe smooth functions but also are flexible and naturally constrained. Two very well-known bioprocess case studies have been successfully addressed by using the new parameterization approach.

Optimal Control of Feeding in Fed-Batch Production of Xylitol

A model-based optimization involving a genetic algorithm was used to establish the optimal substrate feeding profiles in fed-batch fermentations for maximizing the average production rate of xylitol from xylose. The best-case feeding profiles were verified experimentally in fermentations fed with glucose and xylose. The model-predicted profiles agreed remarkably well with the measured data even though the model was based on parameter values derived from a batch fermentation.

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.

Adaptive feedrate interpolation with multiconstraints for five-axis parametric toolpath

A good adaptive feedrate will be helpful for improving machining accuracy and efficiency, as well as avoiding the excess of the machine’s physical capabilities and feed fluctuations during machining. Therefore, it is highly desirable to consider the constraints of geometric error, cutting performance, and drive constraints in the feedrate scheduling of the parametric curve interpolator for five-axis computer numerical control machining. In this paper, a novel multiconstraints feedrate scheduling method is proposed for the parametric curve interpolator in five-axis machining. In the method, the feed optimization model is first built with the constraints of geometric error, the maximum feedrate and acceleration of cutter tip, and the maximum feedrate and acceleration of five-drive axes. Then, the relations between each constraint and the cutter tip feedrate are derived by means of near arc length parameterization. After that, a linear programming algorithm is applied to obtain the optimal feed profile on the sampling positions of the given tool path. Finally, illustrated examples are given to validate the feasibility and applicability of the proposed feedrate scheduling method. The comparison results show that the proposed method has an ability of the simultaneous guarantees of geometric accuracy, cutting performance, and drive characters of machine tools.

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

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. The model parameters and confidence intervals are obtained via a non linear least squares identification. 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). Based on a sensitivity analysis of the model outputs with respect to the parameters, a model reduction is proposed. Finally, the maximization of biomass productivity of hybridoma cell fed-batch cultures is analyzed. This model allows, on the one hand, quantitatively describing overflow metabolism in mammalian cell cultures and, on the other hand, will be valuable for monitoring and control of fed-batch cultures in order to optimize the process. This is illustrated in this contribution with the determination of optimal feeding profiles aiming at maximizing biomass productivity.

Optimization of a Whey Bioprocess using Neuro-Dynamic Programming Strategy

ABSTRACTA method for finding the optimal feeding profile for whey fermentation by strain Kluyveromyces lactic MC 5 in a fed-batch bioreactor was developed. The optimal profile maximizes the process effectiveness and minimizes the bioprocess duration. The method is based on Neuro-dynamic Programming (NDP), wherein the optimal control decision is parameterized in the form of a cost-to-go function. The suggested method employs simulations from a heuristic feeding strategy as an initial point to generate the cost-to-go to experimental data. A neural network is applied to obtain cost-to-go as a function of system state. Iterations of the Bellman equation are included to improve the cost function. Thus, the obtained approach guarantees optimal control of the bioreactor when disturbances are present. The developed approach was compared with other methods—the Pontryagin's Maximum Principle and Fuzzy Sets Theory. The NDP method provided better results than the other methods.

Optimization of Bioethanol Ethanol Production in Fed-batch Fermentation

This study focuses on improving the productivity of a fed-batch ethanol fermentation process by developing and implementing in real time, an optimum feeding policy. A constraint-based stoichiometric model is developed using the systems biology approach, which can quantitatively predict the cellular behavior of the E coli strain, KO11. However, the predictions from this model are accurate under low concentrations of substrate. In order to extend the usage of the model to higher substrate concentrations, we modified this model by introducing changes in glucose utilization rate to restrict the metabolic capacity of the cell. Using the proposed model, the fed-batch optimization problem becomes a constrained optimization problem, and a modified Iterative Dynamic Programming (IDP) algorithm was developed with an adaptive-stage updating methodology, which was applied to solve the global optimization problem. Experiments were carried out based on the optimal feed profile generated using the modified stoichiometric model and the Iterative Dynamic Programming algorithm. Approximately 90% of the theoretical ethanol yield was obtained; the fermentation consumed a total of 521.5 g of glucose and produced 237.5 g of ethanol.

Optimal feeding profile for a fuzzy logic controller in a bioreactors using genetic algorithm

The ultimate objective of any control strategy is to maximize productivity, and improve the quantity of products and reduce costs. The performance of a bioprocess operating in fed batch production of protein can be obtained in two steps. First, we determine the optimal trajectories (profiles) for the variables of interests and then a genetic algorithm based on a fuzzy logic controller is applied to regulate these variables around these profiles.

Influence of fructose and oxygen gradients on fed‐batch recombinant protein production using Bacillus megaterium

AbstractBacillus megaterium expressing a variant of the green fluorescent protein (GFP) was used to investigate the influence of gradients in dissolved oxygen (DO) and fructose concentration on biomass and product formation. For this purpose, several fed‐batch experiments with DO as feed control parameter were performed using suboptimal and optimal adjusted control parameters. In a first approach, suboptimal DO‐feeding was reached by varying randomly the controller output between 10 and 20% of the maximal pumping capacity. This led to fluctuations in DO between 20 and 80% and to substrate gradients around 3 g/L. GFP formation thereby was decreased. In a second approach, an optimal feeding profile was realized using a PI‐control with a constant controller output of 20% was used. Thereby no gradients in substrate concentration, but low‐amplitude and high‐frequency oscillations in the DO concentration were obtained, leading to increased GFP formation. In a final experimental approach, large‐scale conditions were emulated in a two‐compartment scale‐down system consisting of a 3.7‐L stirred tank reactor and a 0.7‐L non‐stirred vessel. DO‐based feeding was applied with the measurement in the 3.7‐L bioreactor and feeding in the small vessel. This setup led to a fairly constant gradient of 20% between both vessels, which also resulted in a decreased GFP productivity.

Application of Dynamic Optimization Techniques for Poly(β-hydroxybutyrate) Production in a Fed-Batch Bioreactor

Poly(β-hydroxybutyrate), PHB, is a microbial biopolymer produced by bacteria under unbalanced culture conditions. Such unbalanced conditions can be easily reached in a fed-batch bioreactor; therefore, it is important to know the system’s behavior as well as its constraints to induce unbalanced conditions that allow the optimization of feeding profiles and, consequently, PHB productivity. In this work, dynamic optimization has been applied to maximize PHB productivity in a fed-batch bioreactor. Optimal feeding profiles of carbon and nitrogen sources, as well as their respective concentrations, were obtained using gPROMS (generalized process modeling system). When there is reliable bioreaction kinetics available, dynamic optimization becomes a very valuable tool for predicting optimal operating conditions to maximize PHB productivity, with a considerable reduction in time and experimental costs.

Optimal feeding profile in fed-batch bioreactors using a genetic algorithm

An optimal feeding profile for a fed-batch process was designed based on an evolutionary algorithm. Usually the presence of multiple objectives in a problem leads to a set of optimal solutions, commonly known as Pareto-optimal solutions. Evolutionary algorithms are well suited for deriving multi-objective optimisation since they evolve a set of non-dominated solutions distributed along the Pareto front. Several evolutionary multi-objective optimisation algorithms have been developed, among which the Non-dominated Sorting Genetic Algorithm NSGA-II is recognised to be very effective in overcoming a variety of problems. To demonstrate the applicability of this technique, an optimal control problem from the literature was solved using several methods considering the single-objective dynamic optimisation problem.