Optimization of fed-batch bioreactor using neural network model

An algorithm using feedforward neural network model for determining optimal substrate feeding policies for fed-batch fermentation process is presented in this work. The algorithm involves developing the neural network model of the process using the sampled data. The trained neural network model in turn is used for optimization purposes. The advantages of this technique is that optimization can be achieved without detailed kinetic model of the process and the computation of gradient of objective function with respect to control variables is straightforward. The application of the technique is demonstrated with two examples, namely, production of secreted protein and invertase. The simulation results show that the discrete-time dynamics of fed-batch bioreactor can be satisfactorily approximated using a feedforward sigmoidal neural network. The optimal policies obtained with the neural network model agree reasonably well with the previously reported results.     

Identification of optimal flow rate for culture media,cell density,and oxygen toward maximization of virus production in a fed-batch baculovirus-insect cell system

In recent times, it has been realized that novel vaccines are required to combat emerging disease outbreaks, and faster optimization is required to respond to global vaccine demands. Although, fed-batch operations offer better productivity, experiment-based optimization of a new fed-batch process remains expensive and time-consuming. In this context, we propose a novel computational framework that can be used for process optimization and control of a fed-batch baculovirus-insect cell system. Since the baculovirus expression vector system (BEVS) is known to be widely used platforms for recombinant protein/vaccine production, we chose this system to demonstrate the identification of optimal profile. Toward this, first, we constructed a mathematical model that captures the time course of cell and virus growth in a baculovirus-insect cell system. Second, the proposed model was used for numerical analysis to determine the optimal operating profiles of control variables such as culture media, cell density, and oxygen based on a multiobjective optimal control formulation. Third, a detailed comparison between batch and fed-batch culture was perfromed along with a comparison between various alternatives of fed-batch operation. Finally, we demonstrate that a model-based quantification of controlled feed addition in fed-batch culture is capable of providing better productivity as compared to a batch culture. The proposed framework can be utilized for the estimation of optimal operating regions of different control variables to achieve maximum infected cell density and virus yield while minimizing the substrate/media, uninfected cell, and oxygen consumption.     

Optimization of biphasic growth of Saccharomyces carlsbergensis in fed-batch culture

The optimal glucose feeding policy for the fed-batch culture of Saccharomyces carlsbergensis is presented. The biphasic nature of growth results in a singular feed rate policy that is unique to this organism. When the operating cost is high, the reduction in operating time forces the cells to utilize both glucose and ethanol toward the end of fermentation time and results in a decreasing rate of glucose addition, unlike the normally observed in creasing feed rate. The optimal feeding policy depends heavily on the initial conditions and is highly sensitive to changes in kinetic parameters. A semiempirical scheme for feedback optimization is suggested for the fed-batch yeast culture.     

An Algorithm for operating a fed-batch fermentation using quasi-steady state

The determination of an optimum feeding profile of a fed-batch fermentation requires the solution of a singular optimum control problem, which is often complicated by changes in the process kinetics during the fermentation. The procedure of optimization may be sufficiently simple, if the feeding part of fermentation is carried out in the quasi-steady state. In this work an algorithm for operating a fed-batch fermentation using mentioned regime is offered. The algorithm supposes a periodical correction of the feeding strategy. Applying to fed-batch lysine fermentation demonstrate efficacy of this algorithm over frequently used strategies.     

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.     

Dynamic optimization of hybridoma growth in a fed-batch bioreactor

This study addressed the problem of maximizing cell mass and monoclonal antibody production from a fed-batch hybridoma cell culture. We hypothesized that inaccuracies in the process model limited the mathematical optimization. On the basis of shaker flask data, we established a simple phenomenological model with cell mass and lactate production as the controlled variables. We then formulated an optimal control algorithm, which calculated the process-model mismatch at each sampling time, updated the model parameters, and re-optimized the substrate concentrations dynamically throughout the time course of the batch. Manipulated variables were feed rates of glucose and glutamine. Dynamic parameter adjustment was done using a fuzzy logic technique, while a heuristic random optimizer (HRO) optimized the feed rates. The parameters selected for updating were specific growth rate and the yield coefficient of lactate from glucose. These were chosen by a sensitivity analysis. The cell mass produced using dynamic optimization was compared to the cell mass produced for an unoptimized case, and for a one-time optimization at the beginning of the batch. Substantial improvements in reactor productivity resulted from dynamic re-optimization and parameter adjustment. We demonstrated first that a single offline optimization of substrate concentration at the start of the batch significantly increased the yield of cell mass by 27% over an unoptimized fermentation. Periodic optimization online increased yield of cell mass per batch by 44% over the single offline optimization. Concomitantly, the yield of monoclonal antibody increased by 31% over the off-line optimization case. For batch and fed-batch processes, this appears to be a suitable arrangement to account for inaccuracies in process models. This suggests that implementation of advanced yet inexpensive techniques can improve performance of fed-batch reactors employed in hybridoma cell culture.     

Optimal nonsingular control of fed-batch fermentation

Presented is a new simple method for multidimensional optimization of fed-batch fermentations based on the use of the orthogonal collocation technique. Considered is the problem of determination of optimal programs for fermentor temperature, substrate concentration in feed, feeding profile, and process duration. By reformulation of the state and control variables is obtained a nonsingular form of the optimization problem which has considerable advantage over the singular case since a complicated procedure for determination of switching times for feeding is avoided. The approximation of the state variables by Lagrange polynomials enables simple incorporation of split boundary conditions in the approximation, and the use of orthogonal collocations provides stability for integration of state and costate variables. The interpolation points are selected to obtain highest accuracy for approximation of the objective functional by the Radau-Lobatto formula. The control variables are determined by optimization of the Hamiltonian at the collocation points with the DFP method. Constraints are imposed on state and control variables.The method is applied for a homogeneous model of fermentation with volume, substrate, biomass, and product concentrations as the state variables. Computer study shows considerable simplicity of the method, its high accuracy for low order of approximation, and efficient convergence.     

Acetopyruvate hydrolase production by Pseudomonas putida O1--optimization of batch and fed-batch fermentations

The main objective of this work was the optimization of the production of the beta-ketolase, acetopyruvate hydrolase, from Pseudomonas putida O1. Orcinol was used as an inducer for enzyme production. The growth medium was optimized in two steps. In the first step, screening for optimal glucose concentration was performed. In the second step, a central composite design was used to optimize carbon and nitrogen sources in the medium. After this optimization procedure, a medium was obtained which produced seven times more biomass than the initial medium. Acetopyruvate hydrolase enzyme production was optimized by determining the optimal time of feed and amount of orcinol, using statistical methods. In a subsequent step, the maximal orcinol-degradation rate was determined. The results obtained were used to find an optimal feeding profile for enzyme production. By using the optimized fed-batch process, acetopyruvate hydrolase activity was enhanced from 10 units l(-1)to 400 units l(-1), in comparison with previously reported fermentation experiments. Productivity could even be increased by a factor of 75, to a value of 20 units l(-1 )h(-1).     

Optimization of feeding profile for baker's yeast production by dynamic programming

An optimal substrate feeding for an industrial scale fed-batch fermenter is determined through iterative dynamic programming in order to maximize the cell-mass production and to minimize the ethanol formation. An experimentally validated rigorous dynamic model comprises constraints in the optimization problem. A new objective function is proposed to accommodate the competing requirements of maximum yeast production and minimum ethanol formation. The objective function is maximized with iterative dynamic programming with respect to the sugar feed rate. Results prove the effectiveness of dynamic programming for solving such high-dimensional and nonlinear optimization problems, and the resulting optimal policy indicates that considerable increase in yeast production in fed-batch fermenters can be achieved while minimizing the undesired by-product, ethanol.     

Dynamic modeling and optimal fed-batch feeding strategies for a two-phase partitioning bioreactor

A dynamic model for the degradation of phenol in a two-phase partitioning bioreactor has been developed based on mechanistic balances around the bioreactor. The key process characteristics including substrate transfer between the organic and aqueous phases, substrate inhibition, oxygen limitation, and cell entrainment were incorporated into the model. The model predictions were validated against existing experimental data obtained for a 2-L bioreactor, and good correlation was observed for the time frames of the simulations, as well as for trends in cell and substrate concentrations. Optimal fed-batch, phenol feeding strategies were then developed based on two approaches: (1) maximization of phenol consumption in a fixed time interval and (2) consumption of a fixed amount of phenol in minimal time. The optimal feeding policies, determined using the Iterative Dynamic Programming algorithm, provided substantial improvements in the amount of phenol consumed when compared to a typical experimental heuristic approach. For example, 45.73 g of phenol was predicted to be consumed in 50 h (not including lag phase) using the optimal feeding profile compared to 10.26 g of phenol consumed in the simulated experimental approach. Oxygen limitation was predicted to be a recurring operational challenge in the partitioning bioreactor, and had a strong impact on the optimization results.     

On-line optimization of recombinant product in a fed-batch bioreactor

In this paper, an efficient scheme for on-line optimization of a recombinant product in a fed-batch bioreactor is presented. This scheme is based on the parametrization of the system states and the elimination of a subset of the dynamic equations in the mathematical model of the fed-batch bioreactor. The fed-batch bioreactor considered here involves the production of chloramphenicol acetyltransferase (CAT) in a genetically modified E. coli. The optimal inducer and the glucose feed rates are obtained using the proposed optimization approach. This approach is compared with the traditional optimization approach, where all the states and the manipulated variables are parametrized. The approach presented in this paper results in a 5-fold improvement in the computational time for the recombinant product optimization. The optimization technique is employed in an on-line optimization scheme, when parametric drift and a disturbance in the manipulated variable is present. Feedback from the process is introduced through resetting the initial conditions of the model and through an observer for estimating the time varying parameter. The simulation results indicated improvement in the amount of product formed, when the optimal profile is regenerated during the course of the batch.     

Optimal feeding strategies by adaptive mesh selection for fed-batch bioprocesses

The objective of this contribution is the design of optimal feeding strategies for fed-batch bioprocesses, where complex dynamic models with input and state constraints are present. For the solution of this dynamic optimization problem a transformation to a finite dimensional optimization problem is made using piecewise linear control profiles. The optimization of these profiles is performed by a sequential approach, that includes an ODE solver for the solution of the model ODE's. Further an adaptive mesh selection algorithm was investigated for an appropriate discretization of the control profiles. The implementation of the resulting optimal feeding profiles is shown for a process example, namely the production of nikkomycin by Streptomyces tendae. This implementation uses a hierarchical process control framework, that consists of components for process monitoring, state estimation, and trajectory control.     

Optimization of fed-batch culture of hybridoma cells using dynamic programming: single and multi feed cases

The optimization of fed-batch culture of hybridoma cells is accomplished on a mathematical model using dynamic programming. Optimal feed trajectories are found using a seventh order model for a single feed stream containing both glucose and glutamine and for two separate feed streams of glucose and glutamine. Compared to a constant feed rate, optimal trajectories can improve the final MAb concentration by 11 % for the single feed case and by 20% for the multifeed case. Higher MAb concentrations can be expected for fed-batch optimization with feed enriched in nutrients.     

Framework for online optimization of recombinant protein expression in high-cell-density Escherichia coli cultures using GFP-fusion monitoring

A framework for the online optimization of protein induction using green fluorescent protein (GFP)-monitoring technology was developed for high-cell-density cultivation of Escherichia coli. A simple and unstructured mathematical model was developed that described well the dynamics of cloned chloramphenicol acetyltransferase (CAT) production in E. coli JM105 was developed. A sequential quadratic programming (SQP) optimization algorithm was used to estimate model parameter values and to solve optimal open-loop control problems for piecewise control of inducer feed rates that maximize productivity. The optimal inducer feeding profile for an arabinose induction system was different from that of an isopropyl-beta-D-thiogalactopyranoside (IPTG) induction system. Also, model-based online parameter estimation and online optimization algorithms were developed to determine optimal inducer feeding rates for eventual use of a feedback signal from a GFP fluorescence probe (direct product monitoring with 95-minute time delay). Because the numerical algorithms required minimal processing time, the potential for product-based and model-based online optimal control methodology can be realized.     

Effects of environmental conditions and methanol feeding strategy on lipase-mediated biodiesel production using soybean oil

Methanol is a commonly used acyl acceptor for lipase-driven biodiesel production, but a high concentration of methanol is detrimental for lipase activity. To overcome this drawback, a simple fed-batch process was developed by optimization of the methanol feeding strategy and reaction conditions. For the feeding strategy, an equal volume of pure methanol was fed twice with specified time intervals into a reactor initially containing a 1:1 molar ratio of soybean oil to methanol in order to adjust the net molar ratio of the oil to methanol to 1:3. In contrast with the batch reaction, a higher agitation speed in the fed-batch process elevated the conversion yield of soybean oil to biodiesel. An agitation speed of 600 rpm and a reaction temperature of 70°C were chosen as the optimal environmental conditions. Residual lipase activities for the fed-batch operation at 40 ∼ 70°C and 600 rpm were 7.1 ± 1.4 times higher than that of the batch method at 40°C with the same agitation speed, indicating that methanol feeding can prevent significant deactivation of lipase. Finally, two times feeding methanol at 2 and 6 hr resulted in a biodiesel productivity of 10.7%/h and 94.9% final conversion yield under the optimal conditions.     

Fed-batch optimization of alpha-amylase and protease-producing Bacillus subtilis using Markov chain methods

A stoichiometry-based model for the fed-batch culture of the recombinant bacterium Bacillus subtilis ATCC 6051a, producing extracellular alpha-amylase as a desirable product and proteases as undesirable products, was developed and verified. The model was then used for optimizing the feeding schedule in fed-batch culture. To handle higher-order model equations (14 state variables), an optimization methodology for the dual-enzyme system is proposed by integrating Pontryagin's optimum principle with fermentation measurements. Markov chain Monte Carlo (MCMC) procedures were appropriate for model parameter and decision variable estimation by using a priori parameter distributions reflecting the experimental results. Using a simplified Metropolis-Hastings algorithm, the specific productivity of alpha-amylase was maximized and the optimum path was confirmed by experimentation. The optimization process predicted a further 14% improvement of alpha-amylase productivity that could not be realized because of the onset of sporulation. Among the decision variables, the switching time from batch to fed-batch operation (t(s)) was the most sensitive decision variable.     

Modeling and optimization of cloned invertase expression in Saccharomyces cerevisiae

The aim of this study is to determine the medium feeding strategy to maximize the invertase productivity of recombinant Saccharomyces Cerevisiae using a fed-batch mode of operation. The yeast contains the plasmid, pRB58, which contains the yeast SUC2 gene, coding for the enzyme invertase. The expression of this gene is repressed at high glucose levels. A Goal-oriented model is development to describe the kinetics of fed-batch fermentations. This simple model could quantitatively describe previous experimental results. A conjugate gradient algorithm is then used, in conjunction gradient algorithm is then used, in conjunction with this mathematical model, to compute the optimum feed rate for maximization of invertase productivity. The optimal feeding procedure results in an initial high cell growth phase followed by a high invertase production phase. (c) 1993 Wiley & Sons, Inc.     

Estimation of optimal feeding strategies for fed-batch bioprocesses

A generic methodology for feeding strategy optimization is presented. This approach uses a genetic algorithm to search for optimal feeding profiles represented by means of artificial neural networks (ANN). Exemplified on a fed-batch hybridoma cell cultivation, the approach has proven to be able to cope with complex optimization tasks handling intricate constraints and objective functions. Furthermore, the performance of the method is compared with other previously reported standard techniques like: (1) optimal control theory, (2) first order conjugate gradient, (3) dynamical programming, (4) extended evolutionary strategies. The methodology presents no restrictions concerning the number or complexity of the state variables and therefore constitutes a remarkable alternative for process development and optimization. This revised version was published online in June 2005 with corrections to the Appendix.     

Optimal Bioreactor Operational Policies for the Enzymatic Hydrolysis of Sugarcane Bagasse

The consolidation of the industrial production of second-generation (2G) bioethanol relies on the improvement of the economics of the process. Within this general scope, this paper addresses one aspect that impacts the costs of the biochemical route for producing 2G bioethanol: defining optimal operational policies for the reactor running the enzymatic hydrolysis of the C6 biomass fraction. The use of fed-batch reactors is one common choice for this process, aiming at maximum yields and productivities. The optimization problem for fed-batch reactors usually consists in determining substrate feeding profiles, in order to maximize some performance index. In the present control problem, the performance index and the system dynamics are both linear with respect to the control variable (the trajectory of substrate feed flow). Simple Michaelis–Menten pseudo-homogeneous kinetic models with product inhibition were used in the dynamic modeling of a fed-bath reactor, and two feeding policies were implemented and validated in bench-scale reactors processing pre-treated sugarcane bagasse. The first approach applied classical optimal control theory. The second policy was defined with the purpose of sustaining high rates of glucose production, adding enzyme (Accellerase® 1500) and substrate simultaneously during the reaction course. A methodology is described, which used economical criteria for comparing the performance of the reactor operating in successive batches and in fed-batch modes. Fed-batch mode was less sensitive to enzyme prices than successive batches. Process intensification in the fed-batch reactor led to glucose final concentrations around 200 g/L.     

Model-based optimization of viral capsid protein production in fed-batch culture of recombinant <Emphasis Type="Italic">Escherichia coli</Emphasis>

An optimized fed-batch cultivation process for the production of the polyoma virus capsid protein VP1 in recombinant Escherichia coli BL21 bacteria is presented. The optimization procedure maximizing the amount of desired protein is based on a mathematical model. The model distinguishes an initial cell growth phase from a protein production phase initiated by inducer injection. A new approach to model the target protein formation rate was elaborated, where product formation is primarily dependent on the specific biomass growth rate. Lower growth rates led to higher specific protein concentrations. The model was identified from a series of fed-batch experiments designed for parameter identification purposes and possesses good prediction quality. Then the model was used to determine optimal open-loop control profiles by manipulating the substrate feed rates in both phases as well as the induction time. Feed-rate optimization has been solved using Pontryagin's maximum principle. The solution was validated experimentally. A significant improvement of the process performance index was achieved.