Dynamic optimization of distributed biological systems using robust and efficient numerical techniques

ABSTRACT: BACKGROUND: Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations. This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. RESULTS: Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. CONCLUSIONS: In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems.     

Phytoremediation: an overview of metallic ion decontamination from soil

In recent years, phytoremediation has emerged as a promising ecoremediation technology, particularly for soil and water cleanup of large volumes of contaminated sites. The exploitation of plants to remediate soils contaminated with trace elements could provide a cheap and sustainable technology for bioremediation. Many modern tools and analytical devices have provided insight into the selection and optimization of the remediation process by plant species. This review describes certain factors for the phytoremediation of metal ion decontamination and various aspects of plant metabolism during metallic decontamination. Metal-hyperaccumulating plants, desirable for heavily polluted environments, can be developed by the introduction of novel traits into high biomass plants in a transgenic approach, which is a promising strategy for the development of effective phytoremediation technology. The genetic manipulation of a phytoremediator plant needs a number of optimization processes, including mobilization of trace elements/metal ions, their uptake into the root, stem and other viable parts of the plant and their detoxification and allocation within the plant. This upcoming science is expanding as technology continues to offer new, low-cost remediation options.     

Kinetic-model-based pathway optimization with application to reverse glycolysis in mammalian cells

Over the last two decades, model-based metabolic pathway optimization tools have been developed for the design of microorganisms to produce desired metabolites. However, few have considered more complex cellular systems such as mammalian cells, which requires the use of nonlinear kinetic models to capture the effects of concentration changes and cross-regulatory interactions. In this study, we develop a new two-stage pathway optimization framework based on kinetic models that incorporate detailed kinetics and regulation information. In Stage 1, a set of optimization problems are solved to identify and rank the enzymes that contribute the most to achieving the metabolic objective. Stage 2 then determines the optimal enzyme interventions for specified desired numbers of enzyme adjustments. It also incorporates multi-scenario optimization, which allows the simultaneous consideration of multiple physiological conditions. We apply the proposed framework to find enzyme adjustments that enable a reverse glucose flow in cultured mammalian cells, thereby eliminating the need for glucose feed in the late culture stage and enhancing process robustness. The computational results demonstrate the efficacy of the proposed approach; it not only captures the important regulations and key enzymes for reverse glycolysis but also identifies differences and commonalities in the metabolic requirements for different carbon sources.     

一种非线性多阶段动力系统的最优控制及数值优化

针对间歇发酵过程的非线性多阶段动力系统,建立了以初始浓度为控制变量、以生产强度为性能指标的最优控制模型.证明了非线性多阶段动力系统的主要性质、最优控制的存在性及达到最优解的必要条件.构造了优化算法并应用于实际数据计算,其数值结果表明了本文模型与算法的有效性.     

Modeling Chlorinated Solvent Bioremediation Using Hydrogen Release Compound (HRC)

Chlorinated solvents such as tetrachloroethene (PCE) and trichloroethene (TCE) are common groundwater contaminants. One approach that has been used to manage these contaminants is in situ bioremediation, where an electron donor is added to contaminated groundwater to stimulate indigenous bacteria to degrade the chlorinated compounds. A technique that is increasingly being used to supply electron donor to the subsurface involves application of a commercial product with the trade name Hydrogen Release Compound (HRC). HRC is a viscous fluid that releases lactic acid, which subsequently is metabolized to provide molecular hydrogen as an electron donor. This study investigates application of HRC to remediate a site contaminated with TCE. A user-defined dual-Monod biodegradation reaction module was developed for the RT3D-reactive transport code to simulate in situ biodegradation of TCE by reductive dehalogenation stimulated by release of molecular hydrogen in the subsurface as a result of HRC injection. The model was used to show how a remediation system using HRC to stimulate reductive dehalogenation could be designed, and how mixing, as quantified by hydraulic conductivity and dispersivity, impacts the system design.     

Time Varying Optimization for Monitoring Multiple Contaminants under Uncertain Hydrogeology

This study presents a method for identifying cost effective sampling designs for long-term monitoring of remediation of groundwater over multiple monitoring periods under uncertain flow conditions. A contaminant transport model is used to simulate plume migration under many equally likely stochastic hydraulic conductivity fields and provides representative samples of contaminant concentrations. Monitoring costs are minimized under a constraint to meet an acceptable level of error in the estimation of total mass for multiple contaminants simultaneously over many equiprobable realizations of hydraulic conductivity field. A new myopic heuristic algorithm (MS-ER) that combines a new error-reducing search neighborhood is developed to solve the optimization problem. A simulated annealing algorithm using the error-reducing neighborhood (SA-ER) and a genetic algorithm (GA) are also considered for solving the optimization problem. The method is applied to a hypothetical aquifer where enhanced anaerobic bioremediation of four toxic chlorinated ethene species is modeled using a complex contaminant transport model. The MS-ER algorithm consistently performed better in multiple trials of each algorithm when compared to SA-ER and GA. The best design of MS-ER algorithm produced a savings of nearly 25% in project cost over a conservative sampling plan that uses all possible locations and samples.     

植物-微生物联合修复毒死蜱污染的土壤

本试验以毒死蜱污染土壤为研究材料,利用降解菌DSP-A分别与高丹草、紫花苜蓿、多花黑麦草进行联合修复,探讨了植物-微生物联合修复毒死蜱污染土壤的效果,以及影响联合修复的因素,结果表明,植物．微生物联合修复的效果优于单一的植物修复及单一的微生物修复效果。与DSP—A菌群较合适的植物是高丹草,该组合对毒死蜱的降解率达到96．44％,其次是多花黑麦草。研究了微生物数量、植株密度以及土壤湿度对联合修复效果的影响,结果表明,DSP．A菌菌液稀释倍数越大,联合修复的效果越差。植株密度对联合修复的影响,主要表现为对植物根系生长的影响。植株密度越大,对生存环境的竞争越激烈,植物根系的生长越不好。除了紫花苜蓿外,高丹草和多花黑麦草根系的生长均受到影响。高丹草种植密度为12株／盆时,与DSP—A菌的联合修复效果最好,多花黑麦草则为10株／盆。土壤湿度是影响联合修复的重要因素,不仅影响植物的生长,对微生物的生长也有影响。土壤湿度过大,造成土壤的含氧量降低,不利于植物根系和好氧细菌的生长,从而影响土壤中农药的降解。土壤湿度过小,容易造成植株缺水,根系生长和微生物的生长。高丹草与DSP．A菌、多花黑麦草与DSP—A菌联合修复最适浇水量都为20mL／d,紫花苜蓿与DSP—A菌联合修复最适浇水量都为15mL／d。     

Time Varying Optimization for Monitoring Multiple Contaminants under Uncertain Hydrogeology

This study presents a method for identifying cost effective sampling designs for long-term monitoring of remediation of groundwater over multiple monitoring periods under uncertain flow conditions. A contaminant transport model is used to simulate plume migration under many equally likely stochastic hydraulic conductivity fields and provides representative samples of contaminant concentrations. Monitoring costs are minimized under a constraint to meet an acceptable level of error in the estimation of total mass for multiple contaminants simultaneously over many equiprobable realizations of hydraulic conductivity field. A new myopic heuristic algorithm (MS-ER) that combines a new error-reducing search neighborhood is developed to solve the optimization problem. A simulated annealing algorithm using the error-reducing neighborhood (SA-ER) and a genetic algorithm (GA) are also considered for solving the optimization problem. The method is applied to a hypothetical aquifer where enhanced anaerobic bioremediation of four toxic chlorinated ethene species is modeled using a complex contaminant transport model. The MS-ER algorithm consistently performed better in multiple trials of each algorithm when compared to SA-ER and GA. The best design of MS-ER algorithm produced a savings of nearly 25% in project cost over a conservative sampling plan that uses all possible locations and samples.     

Investigation of metabolic objectives in cultured hepatocytes

Using optimization based methods to predict fluxes in metabolic flux balance models has been a successful approach for some microorganisms, enabling construction of in silico models and even inference of some regulatory motifs. However, this success has not been translated to mammalian cells. The lack of knowledge about metabolic objectives in mammalian cells is a major obstacle that prevents utilization of various metabolic engineering tools and methods for tissue engineering and biomedical purposes. In this work, we investigate and identify possible metabolic objectives for hepatocytes cultured in vitro. To achieve this goal, we present a special data-mining procedure for identifying metabolic objective functions in mammalian cells. This multi-level optimization based algorithm enables identifying the major fluxes in the metabolic objective from MFA data in the absence of information about critical active constraints of the system. Further, once the objective is determined, active flux constraints can also be identified and analyzed. This information can be potentially used in a predictive manner to improve cell culture results or clinical metabolic outcomes. As a result of the application of this method, it was found that in vitro cultured hepatocytes maximize oxygen uptake, coupling of urea and TCA cycles, and synthesis of serine and urea. Selection of these fluxes as the metabolic objective enables accurate prediction of the flux distribution in the system given a limited amount of flux data; thus presenting a workable in silico model for cultured hepatocytes. It is observed that an overall homeostasis picture is also emergent in the findings.     

Numerical Simulation of Plant–microbial Remediation for Petroleum-polluted Soil

This paper presents a numerical analysis of the migration and transformation mechanism of petroleum hydrocarbons (PHs) pollutants in soil. The mathematical model of the solute migration and plant–microbial remediation for PH polluted soil was established. The model was verified by field experimental data. Then, the software Hydrus-1D was employed to simulate the processes of diffusion, adsorption, desorption, microbial degradation, and plant adsorption of PHs in the soil–water system. The process of plant–microbial remediation for PH-contaminated soil was also simulated. The space-time change of PHs in soil was obtained, and the fate and remediation efficiency of PHs in soil were revealed in different remediation conditions. The results indicated that the Hydrus-1D model can adequately simulate the process of plant–microbial remediation. Plant–microbial remediation appears to be more efficient than the application of bacteria or Suaeda salsa. The majority of PH pollutants are degraded in the upper soil levels. For long-chain petro-alkane-contaminated soil, plant–microbial remediation is a more efficient method. A suitable moisture level in soil is important for improving the bioremediation effect of plant–microbial remediation technology.     

Non-linear control of continuous bioreactors

Control of bioreactors has achieved importance in the recent years. This may be due to the fact that they are difficult to control which may be attributed to its nonlinear dynamic behavior. The model parameters of the bioreactor also vary in an unpredictable manner. The complexity of the biochemical processes inhibits the accurate modeling and also the lack of suitable sensors make the process state difficult to characterize. Considerable emphasis has been placed on the control of fed-batch fermentors because of their prevalence in industries. However, when production of biomass is to be optimized, continuous operation is desirable. Several procedures are available for the nonlinear control of processes, viz., differential geometric approach, internal model control approach, reference synthesis technique, predictive control design, etc., but the major disadvantage of these approaches is the computational time required to perform the prediction optimization. In this study, a nonlinear controller based on a polynomial discrete time model (NARMAX) is evaluated for its performance on a fermentor. It can be shown that a nonlinear self-tuning controller based on NARMAX model can be extended to the control of fermentors. The response is smooth for both load and setpoint changes even when process parameters are assumed to be zero and uncertainty in parameters are present and in the presence of controller constraints. The control action can be made more or less robust by changing the design parameters appropriately. Therefore, nonlinear self-tuning controller is suitable for control of industrial processes.     

Effect of adsorbents on degradation of toxic organic compounds by coimmobilized systems

The use of coimmobilized systems for treatment of toxic organic compounds has been proposed. The proposed approach combines the use of adsorbents and laboratory identified microorganisms immobilized in a protective permeable barrier to achieve a greater degree of control over the remediation process. This study was launched to understand the effect of adsorbents and changes in adsorption on the degradation of toxic compounds by coimmobilized systems. The specific case studied involved the degradation of pentachlorophenol (PCP) by Arthrobacter (ATCC 33790) coimmobilized with powdered activated carbon within calcium alginate capsules.The design parameters studied included adsorbent content and type as well as the effect of solution pH and surfactant concentration on adsorption and biodegradation. It was found that the equilibrium adsorption behavior of PCP was strongly influenced by solution pH and surfactant concentration. A mathematical model was developed that combined the physical processes of mass transfer and adsorption with biological degradation of PCP. The model was used to predict the effect of various parameters on the degradation of PCP. Based on model predictions, the degradation of PCP. Based on model predictions, the degradation of PCP was strongly dependent on variations in adsorbent capacity and affinity for this contaminant.     

Building simulation model of infant-incubator system with decoupling predictive controller

This paper introduces theoretical modelling working on the thermal behavior of the premature infant. This study aims at developing a model useful for the prediction and design of the appropriate controller in objective to reduce evaporative heat loss. A calculation code has been developed to simulate the thermal response of a premature baby to climatic solicitation inside the incubator system. The model allows us to take into consideration radiative, conductive, convective, and evaporative heat transfers inside the incubator system. The air temperature and the humidity rate, which play a salient part in the convective and evaporative exchanges, are calculated by a coupled transfer function. At present, the environmental conditions (temperature and humidity) inside incubator are controlled with a classical Proportional Integral Differential (PID). In this work, we proposed a decoupling Generalized Predictive Controller (DGPC) based on the model described below to achieve an optimal thermal conditions (36.5–37.5) for immature newborn infants (birthweight <1000 grams). Real and simulations results prove the feasibility and effectiveness of the proposed model and controller.     

Kinetic modeling of lipase‐catalyzed esterification reaction between oleic acid and trimethylolpropane: A simplified model for multi‐substrate multi‐product ping–pong mechanisms

Kinetic models are among the tools that can be used for optimization of biocatalytic reactions as well as for facilitating process design and upscaling in order to improve productivity and economy of these processes. Mechanism pathways for multi‐substrate multi‐product enzyme‐catalyzed reactions can become very complex and lead to kinetic models comprising several tens of terms. Hence the models comprise too many parameters, which are in general highly correlated and their estimations are often prone to huge errors. In this study, Novozym^®435 catalyzed esterification reaction between oleic acid (OA) and trimethylolpropane (TMP) with continuous removal of side‐product (water) was carried out as an example for reactions that follow multi‐substrate multi‐product ping‐pong mechanisms. A kinetic model was developed based on a simplified ping‐pong mechanism proposed for the reaction. The model considered both enzymatic and spontaneous reactions involved and also the effect of product removal during the reaction. The kinetic model parameters were estimated using nonlinear curve fitting through unconstrained optimization methodology and the model was verified by using empirical data from different experiments and showed good predictability of the reaction under different conditions. This approach can be applied to similar biocatalytic processes to facilitate their optimization and design. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29:1422–1429, 2013     

An Approach Based on Mutually Informed Neural Networks to Optimize the Generalization Capabilities of Decision Support Systems Developed for Heart Failure Prediction

Available clinical methods for heart failure (HF) diagnosis are expensive and require a high-level of experts intervention. Recently, various machine learning models have been developed for the prediction of HF where most of them have an issue of over-fitting. Over-fitting occurs when machine learning based predictive models show better performance on the training data yet demonstrate a poor performance on the testing data and the other way around. Developing a machine learning model which is able to produce generalization capabilities (such that the model exhibits better performance on both the training and the testing data sets) could overall minimize the prediction errors. Hence, such prediction models could potentially be helpful to cardiologists for the effective diagnose of HF. This paper proposes a two-stage decision support system to overcome the over-fitting issue and to optimize the generalization factor. The first stage uses a mutual information based statistical model while the second stage uses a neural network. We applied our approach to the HF subset of publicly available Cleveland heart disease database. Our experimental results show that the proposed decision support system has optimized the generalization capabilities and has reduced the mean percent error (MPE) to 8.8% which is significantly less than the recently published studies. In addition, our model exhibits a 93.33% accuracy rate which is higher than twenty eight recently developed HF risk prediction models that achieved accuracy in the range of 57.85% to 92.31%. We can hope that our decision support system will be helpful to cardiologists if deployed in clinical setup.     

Hierarchical genetic algorithm for near optimal feedforward neural network design

In this paper, we propose a genetic algorithm based design procedure for a multi layer feed forward neural network. A hierarchical genetic algorithm is used to evolve both the neural networks topology and weighting parameters. Compared with traditional genetic algorithm based designs for neural networks, the hierarchical approach addresses several deficiencies, including a feasibility check highlighted in literature. A multi objective cost function is used herein to optimize the performance and topology of the evolved neural network simultaneously. In the prediction of Mackey Glass chaotic time series, the networks designed by the proposed approach prove to be competitive, or even superior, to traditional learning algorithms for the multi layer Perceptron networks and radial basis function networks. Based upon the chosen cost function, a linear weight combination decision making approach has been applied to derive an approximated Pareto optimal solution set. Therefore, designing a set of neural networks can be considered as solving a two objective optimization problem.