Sensitivity-based adaptive mesh refinement collocation method for dynamic optimization of chemical and biochemical processes

Collocation on finite element (CFE) is an effective simultaneous method of dynamic optimization to increase the profitability or productivity of industrial process. The approach needs to select an optimal mesh of time interval to balance the computational cost with desired solution. A new CFE approach with non-uniform refinement procedure based on the sensitivity analysis for dynamic optimization problems is, therefore, proposed, where a subinterval is further refined if the obtained control parameters have significant effect on the performance index. To improve the efficiency, the sensitivities of state parameters with respect to control parameters are derived from the solution of the discretized dynamic system. The proposed method is illustrated by testing two classic dynamic optimization problems from chemical and biochemical engineering. The detailed comparisons among the proposed method, the CFE with uniform mesh, and other reported methods are also carried out. The research results reveal the effectiveness of the proposed approach.

     

How Biochemical Constraints of Cellular Growth Shape Evolutionary Adaptations in Metabolism

Evolutionary adaptations in metabolic networks are fundamental to evolution of microbial growth. Studies on unneeded-protein synthesis indicate reductions in fitness upon nonfunctional protein synthesis, showing that cell growth is limited by constraints acting on cellular protein content. Here, we present a theory for optimal metabolic enzyme activity when cells are selected for maximal growth rate given such growth-limiting biochemical constraints. We show how optimal enzyme levels can be understood to result from an enzyme benefit minus cost optimization. The constraints we consider originate from different biochemical aspects of microbial growth, such as competition for limiting amounts of ribosomes or RNA polymerases, or limitations in available energy. Enzyme benefit is related to its kinetics and its importance for fitness, while enzyme cost expresses to what extent resource consumption reduces fitness through constraint-induced reductions of other enzyme levels. A metabolic fitness landscape is introduced to define the fitness potential of an enzyme. This concept is related to the selection coefficient of the enzyme and can be expressed in terms of its fitness benefit and cost.     

Productivity improvement in xanthan gum fermentation using multiple substrate optimization

A novel and more comprehensive formulation of the optimal control problem that reflects the operational requirements of a typical industrial fermentation has been proposed in this work. This formulation has been applied to a fed-batch bioreactor with three control variables, i.e., feed rates of carbon source, nitrogen source, and an oxygen source, to result in a 148.7% increase in product formation. Xanthan gum production using Xanthomonas campestris has been used as the model system for this optimization study, and the liquid-phase oxygen supply strategy has been used to supply oxygen to the fermentation. The formulated optimization problem has several constraints associated with it due to the nature of the system. A robust stochastic technique, differential evolution, has been used to solve this challenging optimization problem. The infinite dimensional optimization problem has been approximated to a finite dimensional one by control vector parametrization. The state constraints that are path constraints have been addressed by using penalty functions and by integrating them over the total duration to ensure a feasible solution. End point constraints on final working volume of the reactor and on the final residual concentrations of carbon and nitrogen sources have been included in the problem formulation. Further, the toxicity of the oxygen source, H(2)O(2), has been addressed by imposing a constraint on its maximum usable concentration. In addition, the initial volume of the bioreactor contents and feed concentrations have been handled as decision variables, which has enabled a well-grounded choice for their values from the optimization procedure; adhoc values are normally used in the industry. All results obtained by simulation have been validated experimentally with good agreements between experimental and simulated values.     

Chromatographic capture of cells to achieve single stage clarification in recombinant protein purification

Recent advancements in cell culture engineering have allowed drug manufacturers to achieve higher productivity by driving higher product titers through cell line engineering and high-cell densities. However, these advancements have shifted the burden to clarification and downstream processing where the difficulties now revolve around removing higher levels of process- and product-related impurities. As a result, a lot of research efforts have turned to developing new approaches and technologies or process optimization to still deliver high quality biological products while controlling cost of goods. Here, we explored the impact of a novel single use technology employing chromatographic principle-based clarification for a process-intensified cell line technology. In this study, a 16% economic benefit ($/g) was observed using a single-use chromatographic clarification compared to traditional single-use clarification technology by improving the overall product cost through decreased operational complexity, higher loading capacity, increased product recovery, and higher impurity clearance. In the end, the described novel chromatographic approach significantly simplified and enhanced the cell culture fluid harvest unit operation by combining the reduction of insoluble and key soluble contaminants of the harvest fluid into a single stage.     

Robust and reliable estimation via recursive nonlinear dynamic data reconciliation based on cubature Kalman filter

Since measurements of process variables are subject to measurements errors as well as process variability, data reconciliation is the procedure of optimally adjusting measured date so that the adjusted values obey the conservation laws and constraints. Thus, data reconciliation for dynamic systems is fundamental and important for control, fault detection, and system optimization. Attempts to successfully implement estimators are often hindered by serve process nonlinearities, complicated state constraints, and un-measurable perturbations. As a constrained minimization problem, the dynamic data reconciliation is dynamically carried out to product smoothed estimates with variances from the original data. Many algorithms are proposed to solve such state estimation such as the extended Kalman filter (EKF), the unscented Kalman filter, and the cubature Kalman filter (CKF). In this paper, we investigate the use of CKF algorithm in comparative with the EKF to solve the nonlinear dynamic data reconciliation problem. First we give a broad overview of the recursive nonlinear data dynamic reconciliation (RNDDR) scheme, then present an extension to the CKF algorithm, and finally address the issue of how to solve the constraints in the CKF approach. The CCRNDDR method is proposed by applying the RNDDR in the CKF algorithm to handle nonlinearity and algebraic constraints and bounds. As the sampling idea is incorporated into the RNDDR framework, more accurate estimates can obtained via the recursive nature of the estimation procedure. The performance of the CKF approach is compared with EKF and RNDDR on nonlinear process systems with constraints. The conclusion is that with an error optimization solution of the correction step, the reformulated CKF shows high performance on the selection of nonlinear constrained process systems. Simulation results show the CCRNDDR is an efficient, accurate and stable method for real-time state estimation for nonlinear dynamic processes.     

Process Variety Modeling for Process Configuration in Mass Customization: An Approach Based on Object-Oriented Petri Nets with Changeable Structures

Mass customization strategies could be usefully deployed by companies whose products are characterized by a modular design. Typically, each module serves a specific aspect of the overall product function at varying performance levels. Each product variant (constructed through a unique combination of modular performance levels), therefore, serves to customize the overall performance of the product, thus serving the unique needs of each customer. The high demand for each module guarantees economies of scale and, eventually, low cost to customer. The rationale of configuring production processes for producing individual product variants originates from the fact that massive process data is commonly available in a firm and there exists a generic process structure underlying the production of similar products in a family. To design a decision support mechanism that constructs process configuration corresponding to a given product configuration, this paper develops a formal modeling of process variety using Petri nets. Object-oriented Petri nets (PNs) with changeable structures (OPNs-CS) are applied to deal with the issues of generic representation, constraints compliance, and operational sequence requirements. Object-oriented PN (OPN) models facilitate generic representation of product and process variety as well as their instantiations. The OPNs-CS model is tested with simulation. Based on simulation results, the optimal configuration of production processes can be determined for each individual product as well as the cohort of a product family. To illustrate the feasibility and potential of OPNs-CS based process variety modeling, a case study of process configuration for mass customized textile spindles is reported.     

Selective expression of the soluble product fraction in Escherichia coli cultures employed in recombinant protein production processes

Recombinant proteins produced in Escherichia coli hosts may appear within the cells’ cytoplasm in form of insoluble inclusion bodies (IB’s) and/or as dissolved functional protein molecules. If no efficient refolding procedure is available, one is interested in obtaining as much product as possible in its soluble form. Here, we present a process engineering approach to maximizing the soluble target protein fraction. For that purpose, a dynamic process model was developed. Its essential kinetic component, the specific soluble product formation rate, if represented as a function of the specific growth rate and the culture temperature, depicts a clear maximum. Based on the dynamic model, optimal specific growth rate and temperature profiles for the fed-batch fermentation were determined. In the course of the study reported, the mass of desired soluble protein was increased by about 25%. At the same time, the formation of inclusion bodies was essentially avoided. As the optimal cultivation procedure is rather susceptible to distortions, control measures are necessary to guarantee that the real process can be kept on its desired path. This was possible with robust closed loop control. Experimental process validation revealed that, in this way, high dissolved product fractions could be obtained at an excellent batch-to-batch reproducibility.     

Regime analysis and scale-down: Tools to investigate the performance of bioreactors

Scale-up and optimization of biotechnological processes on a large scale tend to be more methodically approached than the application of rules of thumb, experience, and trial and error. Methods frequently used in chemical engineering are adopted in biochemical engineering and are employed with great effect. A summary is given of methods and rules of thumb used in scaling up chemical processes. A procedure to scale up and optimize bioreactors is presented. It is based on the so-called scale-down approach. Some elements of this procedure, viz. theoretical regime analysis and small-scale investigations, are extensively demonstrated by examples. It is shown that a regime analysis based on characteristic times can give a quick estimation of the performance of bioreactors. Small-scale experiments based on the result of such analysis or on the results of a dimensional analysis can give valuable information for scale-up or optimization fermentation processes.     

Supply chain focus dependent safety stock placement

Increasing globalization, growing product range diversity, and rising consumer awareness are making markets highly competitive, forcing supply chains to adapt constantly to different stimuli. Growing competition between supply chains (as well as players within them) is also warranting a priority for overall supply chain performance over the goals of individual players. It is now well established in the literature that, among the many order winners, both overall supply chain cost and responsiveness (i.e., supply chain lead time) are the most significant determinants of supply chain competitiveness. The literature, however, mostly focuses on supply chain cost minimization with rather simplistic treatment of responsiveness. By introducing the concept of a coefficient of inverse responsiveness (CIR), we facilitate efficient introduction of responsiveness related costs into the scheme of supply chain (SC) performance evaluation and/or optimization. Thus, our model aids supply chain managers in achieving better strategic fit between individual business unit strategies and overall supply chain requirements in terms of cost efficiency and responsiveness. In particular, it aids in strategic placement of safety stocks at different stages in the supply chain. Our model also offers managerial insights that help improve our intuitions into supply chain dynamics. The model is more suited for strategic SC alignment, for example, when dealing with product changeovers or introduction of new product, rather than for operational control.     

Recovery modeling of tangential flow systems

The demand for increased formulation concentrations for protein therapeutics puts a significant strain on already existing tangential flow filtration (TFF) systems that were constructed with lower protein concentration targets as part of their design criteria. TFF is commonly used to buffer exchange and concentrate the product to the appropriate drug substance concentration. Analyzing the ability of an existing TFF system to process under conditions outside its original design specifications can be challenging. In this analysis, we present a systematic approach to assess the operational limits of a TFF process with consideration of system performance parameters for changing process targets. In two new engineering diagrams, the recovery efficiency diagram and the operating space plot, all relevant operational constraints and parameters are related to allow rapid process fit evaluation. The engineering assessment of TFF systems presented in this article allows a rational review of system limitations during process fit evaluations of existing TFF systems. It also provides a rational basis for targeted system upgrades and setting system design specifications for the design of new systems if existing systems are found inadequate. Biotechnol. Bioeng. 2012; 109: 3084–3092. © 2012 Wiley Periodicals, Inc.     

Trade-off Modeling for Product and Manufacturing Process Design for the Environment

This article presents a method for integrating pollution prevention and concurrent engineering (simultaneous design of products and the manufacturing processes used to produce them). The central issue is unavoidable trade-offs, such as those among pollution, manufacturing cost, and quality. The probabilistic nature of the manufacturing process is exploited as an opportunity for pollution preventi0n.A decision tool in the form of a mathematical model is presented, which can be used by engineers and others with whom these trade-offs must be negotiated, Specifically, the method integrates statistical manufacturing process control into a mubobjective design optimization formulation. First, the framework of a multiattribute utilty function is developed to determine which objectives are both relevant and negotiable. Then, a statistical manufacturing process control experiment is conducted to formulate some of the constraints that prevent all objectives from being maximized. Simultaneously, information obtained from the experiment is also used to fine-tune the upper and lower bounds in the utility functions. The results of an industrial case study of a floor tile manufacturer are presented, from the manufacturer's viewpoint. The material choice and manufacturing process settings that result in the best combination of the conflicting objectives of product quality (measured in terms of scrap rate), air pollution, and manufacturing cost are determined. The analysis also reveals the irony that for this manufacturer; efforts to reduce solid waste through greater use of scrap materials increase air pollution levels     

Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et?al., J Math Biol 61(3):423?C453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem.     

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.     

Improving the batch-to-batch reproducibility in microbial cultures during recombinant protein production by guiding the process along a predefined total biomass profile

In industry Escherichia coli is the preferred host system for the heterologous biosynthesis of therapeutic proteins that do not need posttranslational modifications. In this report, the development of a robust high-cell-density fed-batch procedure for the efficient production of a therapeutic hormone is described. The strategy is to guide the process along a predefined profile of the total biomass that was derived from a given specific growth rate profile. This profile might have been built upon experience or derived from numerical process optimization. A surprisingly simple adaptive procedure correcting for deviations from the desired path was developed. In this way the batch-to-batch reproducibility can be drastically improved as compared to the process control strategies typically applied in industry. This applies not only to the biomass but, as the results clearly show, to the product titer also.     

Defining process design space for monoclonal antibody cell culture

The concept of design space has been taking root as a foundation of in‐process control strategies for biopharmaceutical manufacturing processes. During mapping of the process design space, the multidimensional combination of operational variables is studied to quantify the impact on process performance in terms of productivity and product quality. An efficient methodology to map the design space for a monoclonal antibody cell culture process is described. A failure modes and effects analysis (FMEA) was used as the basis for the process characterization exercise. This was followed by an integrated study of the inoculum stage of the process which includes progressive shake flask and seed bioreactor steps. The operating conditions for the seed bioreactor were studied in an integrated fashion with the production bioreactor using a two stage design of experiments (DOE) methodology to enable optimization of operating conditions. A two level Resolution IV design was followed by a central composite design (CCD). These experiments enabled identification of the edge of failure and classification of the operational parameters as non‐key, key or critical. In addition, the models generated from the data provide further insight into balancing productivity of the cell culture process with product quality considerations. Finally, process and product‐related impurity clearance was evaluated by studies linking the upstream process with downstream purification. Production bioreactor parameters that directly influence antibody charge variants and glycosylation in CHO systems were identified. Biotechnol. Bioeng. 2010;106: 894–905. © 2010 Wiley Periodicals, Inc.     

Potential of the pseudo-inverse method as a constrained static optimization for musculo-tendon forces prediction

Inverse dynamics combined with a constrained static optimization analysis has often been proposed to solve the muscular redundancy problem. Typically, the optimization problem consists in a cost function to be minimized and some equality and inequality constraints to be fulfilled. Penalty-based and Lagrange multipliers methods are common optimization methods for the equality constraints management. More recently, the pseudo-inverse method has been introduced in the field of biomechanics. The purpose of this paper is to evaluate the ability and the efficiency of this new method to solve the muscular redundancy problem, by comparing respectively the musculo-tendon forces prediction and its cost-effectiveness against common optimization methods. Since algorithm efficiency and equality constraints fulfillment highly belong to the optimization method, a two-phase procedure is proposed in order to identify and compare the complexity of the cost function, the number of iterations needed to find a solution and the computational time of the penalty-based method, the Lagrange multipliers method and pseudo-inverse method. Using a 2D knee musculo-skeletal model in an isometric context, the study of the cost functions isovalue curves shows that the solution space is 2D with the penalty-based method, 3D with the Lagrange multipliers method and 1D with the pseudo-inverse method. The minimal cost function area (defined as the area corresponding to 5% over the minimal cost) obtained for the pseudo-inverse method is very limited and along the solution space line, whereas the minimal cost function area obtained for other methods are larger or more complex. Moreover, when using a 3D lower limb musculo-skeletal model during a gait cycle simulation, the pseudo-inverse method provides the lowest number of iterations while Lagrange multipliers and pseudo-inverse method have almost the same computational time. The pseudo-inverse method, by providing a better suited cost function and an efficient computational framework, seems to be adapted to the muscular redundancy problem resolution in case of linear equality constraints. Moreover, by reducing the solution space, this method could be a unique opportunity to introduce optimization methods for a posteriori articulation of preference in order to provide a palette of solutions rather than a unique solution based on a lot of hypotheses.     

Progress in monitoring, modeling and control of bioprocesses during the last 20 years

The paper gives a review on the recent development of bioprocess engineering. It includes monitoring of product formation processes by flow injection analysis, various types of chromatographic and spectroscopic methods as well as by biosensors. The evaluation of mycelial morphology and physiology by digital image analysis is discussed also. It deals with advanced control of indirectly evaluated process variables by means of state estimation/observer, with the use of structured and hybrid models, expert systems and pattern recognition for process optimization and gives a short report on the state of the art of metabolic flux analysis and metabolic engineering.     

Performance modeling and simulation of biochemical process sequences with interacting unit operations

Many biochemical processes consist of a sequence of operations for which optimal operating conditions (setpoints) have to be determined. If such optimization is performed for each operation separately with respect to objectives defined for each operation individually, overall process performance is likely to be suboptimal. Interactions between unit operations have to be considered, and a unique objective has to be defined for the whole process. This paper shows how a suitable optimization problem can be formulated and solved to obtain the best overall set of operating conditions for a process. A typical enzyme production process has been chosen as an example. In order to arrive at a demonstrative model for the entire sequence of unit operations, it is shown how interaction effects may be accommodated in the models. Optimal operating conditions are then determined subject to a global process objective and are shown to be different from those resulting from optimization of each separate operation. As this strategy may result in an economic benefit, it merits further research into interaction modeling and performance optimization.     

Cell culture processes for monoclonal antibody production

Animal cell culture technology has advanced significantly over the last few decades and is now generally considered a reliable, robust and relatively mature technology. A range of biotherapeutics are currently synthesized using cell culture methods in large scale manufacturing facilities that produce products for both commercial use and clinical studies. The robust implementation of this technology requires optimization of a number of variables, including (1) cell lines capable of synthesizing the required molecules at high productivities that ensure low operating cost; (2) culture media and bioreactor culture conditions that achieve both the requisite productivity and meet product quality specifications; (3) appropriate on-line and off-line sensors capable of providing information that enhances process control; and (4) good understanding of culture performance at different scales to ensure smooth scale-up. Successful implementation also requires appropriate strategies for process development, scale-up and process characterization and validation that enable robust operation and ensure compliance with current regulations. This review provides an overview of the state-of-the art technology in key aspects of cell culture, e.g., generation of highly productive cell lines and optimization of cell culture process conditions. We also summarize the current thinking on appropriate process development strategies and process advances that might affect process development.Key words: monoclonal antibody, expression systems, cell line engineering, cell culture process development, optimization scale-up and technology transfer, process advances